1. Solving Quadratic Equations
by Finding Square Roots
Chapter 4.5

2. Format
d
• x
• To solve take square root of both
sides
2

x2
x
d
d

3. Examples
x
2
x
36
2
x
x
36
6
2
x
x
2
7
7
7

4. Solution Types
• x
2
d
When d is positive
 2 solutions
When d is zero
 One solution
When d is negative
 No Real solutions

5. Solve equations using square rooting!
Goal:
x 2 term
• Isolate the
• Leave answers in exact form
2
2
• Examples
x 8 3x 10
-3x2
-3x2
2
2x
2
x
x
2
50
2
25
5
2x
2
8
10
-8
2x
2
x
x
2
-2
-8
18
-2
9
3

6. 4x
2
2 5
+2
4x
4
x
2
2
+2
4 x 1
4
x 1
4
7
4
x 1
x
x
7
2
8
4
7
7
4
2
x 1
+1
x
2
2
2
2
2
+1
2 1

7. Falling Objects
• Formula
 h
16t 2
s
 h = height of object (at end of fall)
 s = height the object was dropped from
 t = # of seconds object has fallen
Word problems!

8. Example
For a science competition students
designed a container that prevents an
egg from breaking when dropped
from a height of 50 ft. How long does
the container take to hit the ground?
(round answer to nearest tenth)
• h = 0 ft
• s = 50 ft
• t = What we need to calculate
h
16t
2
s
0
16t
2
50

9. 0
16t
+16t2
16
t
25
8
50
+16t2
16t
t
2
2
t
2
50
16
50
16
25
8
5
2 2
t 1.8 seconds