1. Solving the Quadratic Equation by Completing the Square
10.7
Solving the Quadratic Equation by Completing the Square

2. How would you factor x2-6x+7=0?
Complete the square when the leading coefficient is 1.

3. Steps to “Completing the Square”
Subtract “c” from both sides of the equal sign.
Find (1/2b)2
Add that 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.

4. x2-6x+7=0 X2 - 6x =-7 x2-6x+9=-7+9 Subtract 7
Practice the steps to 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
Make perfect square trinomial

5. Tip: Put ½ b into the ( ) with sign from original.
(x-3)2=2
Take sq. root
Add 3 to both sides
Two Answers

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

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

8. Solve when the coefficient isn’t 1!
4x2-4x-15=0
Original: divide each term by 4 to get x2 alone.

9. (x- )2 = 4
x =  2 +

10. What method is best?