1. Do Now
Factor the expression.
x2 + 18x + 81
x2 - 22x + 121

2. Objective: solve quadratic equations by completing the square

3. Completing the Square
Find the value of c that makes x2 - 6x + c a perfect square trinomial. Then write the expression as the square of a binomial.
To find the value of c, use the “b” value (ax2+bx+c):
Find half the coefficient of x.
Square the result of Step 1.
Replace c with the result of Step 2.
Answer:
½ (– 6) =
(– 3)2 =
x2 – 6x + 9
when c = 9, x2 – 6x + 9 = (x – 3)2

4. Example: Completing the Square
Find the value of c that makes x2 - 12x + c a perfect square trinomial. Then write the expression as the square of a binomial.
To find the value of c, use the “b” value (ax2+bx+c):
Find half the coefficient of x.
Square the result of Step 1.
Replace c with the result of Step 2.
Answer:

5. Practice
Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.
x2 + 8x + c
x2 - 14x + c
x2 - 10x + c
x2 + 18x + c

6. Solving Quadratics

7. Example

8. Solve the equation by completing the square.
x2 + 2x – 3 = 0
x2 - 6x + 16 = 0

9. Solve the equation by completing the square.
x2 - 8x - 20 = 0
x2 + 4x - 15 = 21

10. Solve the equation by completing the square.
x2 - 2x - 2 = 0
x2 + 6x + 3 = 0

11. Homework
Completing the Square Worksheet