1. 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 x2 + 6x3
Take half of the coefficient of ‘x’
Square it and add it 9
x2 + 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.) If the quadratic does not factor, move the
constant to the other side of the equation
Ex: x²-4x -7 = x²-4x=7
2.) Work with the x²+ x side of the equation and
complete the square by taking ½ of the coefficient
of x and squaring
Ex. x² -4x /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 your trinomial square
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+9

7. Solve by Completing the Square
+121

8. Solve by Completing the Square+1

9. Solve by Completing the Square
+25

10. Solve by Completing the Square
+16

11. Solve by Completing the Square+9

12. The coefficient of x2 must be “1”

13. The coefficient of x2 must be “1”