1. 1.7 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square

2. Steps to complete the square 1.) You will get an expression that looks like this: ax²+ bx 2.) Our goal is to make a square such that we have (a + b)² = a² +2ab + b² 3.) We take ½ of the X coefficient (Divide the number in front of the X by 2) 4.) Then square that number

3. To Complete the Square x 2 + 6x Take half of the coefficient of ‘x’ Square it and add it 3 9 x 2 + 6x + 9 = (x + 3) 2

4. Complete the square, and show what the perfect square is:

5. Steps to solve by completing the square 1.) Move the constant to the other side of the equation Ex: x²-4x -7 =0 x²-4x=7 2.) Take ½ of the coefficient of x (b-value) and square it Ex. x² - 4x+ ___ 4/2= 2²=4 3.) Add the number you got to complete the square to both sides of the equation Ex: x² -4x +4 = 7 +4 4.)Simplify into factored form. (It will always be the value you have right before you “square it”) Ex: (x - 2)² =11 5.)Take the square root of both sides of the equation Ex: x-2 = ±√11 6.) Solve for x Ex: x= 2 ±√11

6. Solve by Completing the Square

11. The coefficient of x 2 must be “1”

14. Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers.