This document provides examples and explanations for factoring quadratic expressions using the method of completing the square. It begins with 6 expressions to factor. Then it discusses what completing the square means, provides examples of perfect square trinomials, and walks through examples of solving quadratics by completing the square. It discusses the different types of solutions that can be obtained. Finally, it provides practice problems for students to solve on their own and discusses the homework assigned.

1. Opener: Write the following expressions as products.
Please get out your 1.) x2 ‐ 12x + 35 2.)x4 ‐ 12x2 ‐ 64
rough drafts &
writing assignment
sheets for the
progress check.
3.)x2 ‐ 5x ‐ 84 4.) x2 ‐ 8x ‐ 20
5.) x4‐196y2 6.) ‐256 +81x20
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3. Homework
Questions:
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4. Section 7.12 Factoring by Completing the Square
Topic One:
We can solve x2 ‐ 9 =0 using DOTS.
Factoring by
Completing the
Square
We can solve (x+4)2 ‐ 9 = 0 also using DOTS.
How could we use DOTS for (x ‐ 5)2 ‐ 7 = 0?
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5. Section 7.12 Factoring by Completing the Square
Topic One: What does it mean to complete the square?
Factoring by
Completing the
Square
What is a perfect square trinomial?
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6. Topic One: (Ex. 1) Solve x2‐ 66x = ‐945 by completing the square.
Factoring by Completing the Square ‐ DOTS
Completing the Step One: Get the equation in Normal Form and equal
Square to zero.
Step Two: Half the coefficient of x. Square your result and
add it to the first two terms.
Step Three: Rewrite your polynomial using DOTS and
by fixing the constant term.
Step Four: Solve using ZPP.
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7. Topic One: (Ex. 1) Solve x2‐ 66x = ‐945 by completing the square.
Factoring by Completing the Square ‐ Square Root
Completing the
Square Step One: Get the constant alone on one side of
equation.
Step Two: Build a perfect square trinomial. (* Be careful
to add new constant to BOTH sides of the equation!)
Step Three: Solve your equation.
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8. Topic One: (Ex. 2) Solve x2 + 120 = 23x by completing the square.
Factoring by
Completing the
Square
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9. Topic One:
It's Your Turn!!! Solve each of the following quadratics using completing
the square.
(Ex. 3 & 4) x2 + 19x + 84 = 0 x2 ‐ 8x + 15 = 0
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10. Topic Two: Will types of solutions can we expect when solving
quadratics?
Quadratic Solutions
Solve each of the following using completing the
square.
(Ex. 5) x2 ‐ 24x = ‐ 200
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(Ex. 6) x + 24x + 42 = 0
(Ex. 7) x2 ‐ 12x + 45 = 0
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11. Topic Two: Let's apply our findings from before to these examples.
Quadratic Solutions
(Ex. 8) For what values of c does x2 ‐ 66x + c = 0 have the
following results?
a. two distinct integer solutions
b. only one integer solutions
c. no integer solutions
It's Your Turn!!!
(Ex. 9 ) For what values of c does x2 ‐ 35x + c = 0 have the
Discuss Ex. 9 with following results?
your partner.
a. one distinct solution
b. only one solution
c. no Real number solutions
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12. Homework: • Pg. 666 # 1, 2, 5, 7, 14, 20, 22 (as is on assignment
sheet)
• Study for 7.11 Mini Quiz
• Rough Draft # 2 for Writing Assignment 2
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