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

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

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.

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

Tip: Put ½ b into the ( ) with sign from original. (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 the coefficient isn’t 1! 4x2-4x-15=0 Original: divide each term by 4 to get x2 alone.

(x- )2 = 4 x =  2 +

What method is best?