Solving the Quadratic Equation by Completing the Square

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

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

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.

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

(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

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

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

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

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

9x2-18x-12=0