1. Solving the Quadratic Equation by Completing the Square

2. Ways To Solve a Quadratic Equation
Graph and the x-intercepts are the solutions (“zeros”)
Factor to solve
Use the quadratic formula
Complete the Square
Use when you can’t factor easily

3. How would you factor x2-6x+7=0?
You can’t, it’s prime
Solve by Completing the Square

5. Steps to “Completing the Square”
(Starting from standard form)
Subtract “c” from both sides of the equal sign. (no longer in standard form)
Find (1/2b)2
Add (1/2b)2 value to both sides of the equal sign.
Factor the perfect square trinomial.
Tip: Substitute the value of “1/2b” into the parentheses to make a perfect square trinomial. (x + ___)2 = {c + (1/2b)2}
Take the square root of both sides.
Solve for x.

6. x2-6x+7=0 X2 - 6x =-7 x2-6x+9=-7+9 Subtract 7
Practice completing the square.
x2-6x+7=0
X2 - 6x =-7
Subtract 7
Add (½ b)2 to each side.
(1/2(-6))2 = 9
x2-6x+9=-7+9
It should make a perfect square trinomial on the left

7. (x-3)2=2 Two Answers Now factor the perfect square trinomial
Tip: Put ½ b into the ( ) with sign from original and simplify the right
(x-3)2=2
Take sq. root
Add 3 to both sides
Two Answers

8. x2+5x-8=0 PRACTICE x2 + 5x = 8 (1/2∙5)2 = 25/4 = 6¼

9. Practice: x2-4x+2=0 x2 - 4x = -2 (1/2 (-4))2 = 4 x2 - 4x + 4 = -2 + 4

10. Solve when a isn’t 1! 4x2-4x-15=0 Divide each term by a
-divide each term by 4 to get x2 alone, then solve

11. 4x2-4x-15=0
x2- x- = 0
(x- )2 = 4
x =  2 +
x = 2 ½ & -1 ½

12. 9x2-18x-12=0