The document discusses how to solve radical equations by squaring both sides of the equation repeatedly to remove radicals. Key steps include:
1) Isolating the radical term to one side of the equation before squaring.
2) Using the identity (a ± b)2 = a2 ± 2ab + b2 to expand squared terms.
3) Squaring both sides and solving the resulting non-radical equation for the variable.
4) Checking that solutions satisfy the original radical equation. Examples demonstrate these techniques.
I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
Factor Theorem and Remainder Theorem. Mathematics10 Project under Mrs. Marissa De Ocampo. Prepared by Danielle Diva, Ronalie Mejos, Rafael Vallejos and Mark Lenon Dacir of 10- Einstein. CNSTHS.
Quadratic equations are explained in simple steps to meet your level of understanding. Please provide feedback so we improve our program for your learning benefit.
Factor Theorem and Remainder Theorem. Mathematics10 Project under Mrs. Marissa De Ocampo. Prepared by Danielle Diva, Ronalie Mejos, Rafael Vallejos and Mark Lenon Dacir of 10- Einstein. CNSTHS.
Quadratic equations are explained in simple steps to meet your level of understanding. Please provide feedback so we improve our program for your learning benefit.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Search and Society: Reimagining Information Access for Radical FuturesBhaskar Mitra
The field of Information retrieval (IR) is currently undergoing a transformative shift, at least partly due to the emerging applications of generative AI to information access. In this talk, we will deliberate on the sociotechnical implications of generative AI for information access. We will argue that there is both a critical necessity and an exciting opportunity for the IR community to re-center our research agendas on societal needs while dismantling the artificial separation between the work on fairness, accountability, transparency, and ethics in IR and the rest of IR research. Instead of adopting a reactionary strategy of trying to mitigate potential social harms from emerging technologies, the community should aim to proactively set the research agenda for the kinds of systems we should build inspired by diverse explicitly stated sociotechnical imaginaries. The sociotechnical imaginaries that underpin the design and development of information access technologies needs to be explicitly articulated, and we need to develop theories of change in context of these diverse perspectives. Our guiding future imaginaries must be informed by other academic fields, such as democratic theory and critical theory, and should be co-developed with social science scholars, legal scholars, civil rights and social justice activists, and artists, among others.
Let's dive deeper into the world of ODC! Ricardo Alves (OutSystems) will join us to tell all about the new Data Fabric. After that, Sezen de Bruijn (OutSystems) will get into the details on how to best design a sturdy architecture within ODC.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
2. Radical equations are equations with the unknown x under
the radical.
Radical Equations
3. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
Radical Equations
4. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
5. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals.
6. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
7. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4
8. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4 square each side
9. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4 square each side
(x)2 = 42
10. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4 square each side
(x)2 = 42
x = 16
11. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4 square each side
(x)2 = 42
x = 16 It works.
12. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4 square each side
(x)2 = 42
x = 16 It works.
b. x – 3 = 4
13. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4 square each side
(x)2 = 42
x = 16 It works.
b. x – 3 = 4 square each side
14. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4 square each side
(x)2 = 42
x = 16 It works.
b. x – 3 = 4 square each side
(x – 3)2 = 42
15. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4 square each side
(x)2 = 42
x = 16 It works.
b. x – 3 = 4 square each side
(x – 3)2 = 42
x – 3 = 16
x = 19
16. Radical equations are equations with the unknown x under
the radical.
To solve radical equations, we use the following fact.
If L=R, then L2 = R2.
Radical Equations
To solve a radical equation, square each side of the equation
(repeatedly if necessary) to remove the radicals. Then solve
for x and check the answers.
Example A. Solve.
a. x = 4 square each side
(x)2 = 42
x = 16 It works.
b. x – 3 = 4 square each side
(x – 3)2 = 42
x – 3 = 16
x = 19 It works.
18. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
Radical Equations
19. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
2x + 1 = 9
Radical Equations
20. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
2x + 1 = 9
2x = 8
Radical Equations
21. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
2x + 1 = 9
2x = 8
x = 4
Radical Equations
22. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
2x + 1 = 9
2x = 8
x = 4
However, x = 4 does not work. So there is no solution.
Radical Equations
23. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
2x + 1 = 9
2x = 8
x = 4
However, x = 4 does not work. So there is no solution.
Radical Equations
For some problems, we have to square more than once to
eliminate all the radicals.
24. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
2x + 1 = 9
2x = 8
x = 4
However, x = 4 does not work. So there is no solution.
Radical Equations
For some problems, we have to square more than once to
eliminate all the radicals. Recall the squaring formula that
(A ± B)2 A2 ± 2AB + B2
25. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
2x + 1 = 9
2x = 8
x = 4
However, x = 4 does not work. So there is no solution.
Radical Equations
Example B. Expand.
a. (x + 4)2
For some problems, we have to square more than once to
eliminate all the radicals. Recall the squaring formula that
(A ± B)2 A2 ± 2AB + B2
Let’s review the algebra below.
26. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
2x + 1 = 9
2x = 8
x = 4
However, x = 4 does not work. So there is no solution.
Radical Equations
Example B. Expand.
a. (x + 4)2
= (x )2 + 2 * 4 x + 42
For some problems, we have to square more than once to
eliminate all the radicals. Recall the squaring formula that
(A ± B)2 A2 ± 2AB + B2
Let’s review the algebra below.
27. c. 2x + 1 = –3 square each side
(2x + 1)2 = (–3)2
2x + 1 = 9
2x = 8
x = 4
However, x = 4 does not work. So there is no solution.
Radical Equations
Example B. Expand.
a. (x + 4)2
= (x )2 + 2 * 4 x + 42
= x + 8x + 16
For some problems, we have to square more than once to
eliminate all the radicals. Recall the squaring formula that
(A ± B)2 A2 ± 2AB + B2
Let’s review the algebra below.
32. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
33. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
34. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
35. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
36. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
37. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
8x = 4x – 12
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
38. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
8x = 4x – 12 divide by 4
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
39. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
8x = 4x – 12 divide by 4
2x = x – 3
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
40. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
8x = 4x – 12 divide by 4
2x = x – 3 square again
( 2x)2 = (x – 3)2
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
41. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
8x = 4x – 12 divide by 4
2x = x – 3 square again
( 2x)2 = (x – 3)2
4x = x2 – 2*3x + 9
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
42. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
8x = 4x – 12 divide by 4
2x = x – 3 square again
( 2x)2 = (x – 3)2
4x = x2 – 2*3x + 9
0 = x2 – 10x + 9
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
43. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
8x = 4x – 12 divide by 4
2x = x – 3 square again
( 2x)2 = (x – 3)2
4x = x2 – 2*3x + 9
0 = x2 – 10x + 9 0 = (x – 9)(x – 1)
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
44. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
8x = 4x – 12 divide by 4
2x = x – 3 square again
( 2x)2 = (x – 3)2
4x = x2 – 2*3x + 9
0 = x2 – 10x + 9 0 = (x – 9)(x – 1)
x = 9 or x = 1
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
45. Radical Equations
b. (2x + 1 – 3)2
= (2x + 1)2 – 2*32x + 1 + 32
= 2x + 1 – 62x + 1 + 9
= 2x + 10 – 62x+1
Example C. Solve for x.
a. x + 4 = 5x + 4 square both sides
(x + 4)2 = (5x + 4 )2
x + 2*4 x + 16 = 5x + 4 isolate the radical
8x = 4x – 12 divide by 4
2x = x – 3 square again
( 2x)2 = (x – 3)2
4x = x2 – 2*3x + 9
0 = x2 – 10x + 9 0 = (x – 9)(x – 1)
x = 9 or x = 1 Only 9 is good.
When squaring both sides of an equation to remove a radical,
make sure that the radical term is isolated to one side first.
48. b. x + 1 – 3 = x – 8 square both sides;
(x + 1 – 3)2 = (x – 8)2
x + 1 – 2*3x + 1 + 32 = x – 8
Radical Equations
49. b. x + 1 – 3 = x – 8 square both sides;
(x + 1 – 3)2 = (x – 8)2
x + 1 – 2*3x + 1 + 32 = x – 8
x + 10 – 6x + 1 = x – 8
Radical Equations
50. b. x + 1 – 3 = x – 8 square both sides;
(x + 1 – 3)2 = (x – 8)2
x + 1 – 2*3x + 1 + 32 = x – 8
x + 10 – 6x + 1 = x – 8 isolate the radical
Radical Equations
51. b. x + 1 – 3 = x – 8 square both sides;
(x + 1 – 3)2 = (x – 8)2
x + 1 – 2*3x + 1 + 32 = x – 8
x + 10 – 6x + 1 = x – 8 isolate the radical
10 + 8 = 6x + 1
Radical Equations
52. b. x + 1 – 3 = x – 8 square both sides;
(x + 1 – 3)2 = (x – 8)2
x + 1 – 2*3x + 1 + 32 = x – 8
x + 10 – 6x + 1 = x – 8 isolate the radical
10 + 8 = 6x + 1
18 = 6x + 1
Radical Equations
53. b. x + 1 – 3 = x – 8 square both sides;
(x + 1 – 3)2 = (x – 8)2
x + 1 – 2*3x + 1 + 32 = x – 8
x + 10 – 6x + 1 = x – 8 isolate the radical
10 + 8 = 6x + 1
18 = 6x + 1 div. by 6
3 = x + 1
Radical Equations
54. b. x + 1 – 3 = x – 8 square both sides;
(x + 1 – 3)2 = (x – 8)2
x + 1 – 2*3x + 1 + 32 = x – 8
x + 10 – 6x + 1 = x – 8 isolate the radical
10 + 8 = 6x + 1
18 = 6x + 1 div. by 6
3 = x + 1 square again
32 = (x + 1)2
Radical Equations
55. b. x + 1 – 3 = x – 8 square both sides;
(x + 1 – 3)2 = (x – 8)2
x + 1 – 2*3x + 1 + 32 = x – 8
x + 10 – 6x + 1 = x – 8 isolate the radical
10 + 8 = 6x + 1
18 = 6x + 1 div. by 6
3 = x + 1 square again
32 = (x + 1)2
9 = x + 1
8 = x This answer is good.
Radical Equations
56. Radical Equations
Exercise A. Isolate the radical then solve for x by squaring
both sides. Make sure to check your answers.
1. x = 3 2. x + 3 = 0 3. x – 5 = 3
5. 2x – 3 = 3
4. x – 5 = 3
6. 2x – 3 = 3 7. 2x – 3 = 3
8. 4x – 1 = 3 9. 4x – 1 = 3 10. 2x – 3 = – 3
11. 23x – 1 + 3 = 7 12. 4 – 33 – 2x = 1
13. x2 – 8 – 1 = 0 14. x2 – 8x – 3 = 0
Exercise B. Isolate one radical if needed, square. Then do it
again to solve for x. Make sure to check your answers.
15. x – 2 = x – 4 16. x + 3 = x + 1
17. 2x – 1 = x + 5 18. 4x + 1 – x + 2 = 1
19. x – 2 = x + 3 – 1 20. 3x + 4 = 3 – x – 1
21. 2x + 5 = x + 4 22. 5 – 4x – 3 – x = 1
57. Radical Equations
25. Given that (x, 4) is the distance of 5 from the origin
(0, 0). Find x and draw the points.
26. Find y where the points (2, y) is the distance of 5 from
(–1 , –1). Draw the points.
23. Given that (x, 0) has the same distance to (0, 2) as to
the point (2, –2). Find x and draw.
24. Given that (0, y) has the same distance to (3, 0) as to
the point (2, 1). Find x and draw.
Exercise C. Use the distance formula D = √Δx2 + Δ y2
to solve the following distance problems.
