1. Algebra 1 Jarrett Sutter
10.5 Completing the Square
Algebra 1 Jarrett Sutter

2. Ways to Solve a Quadratic
Factor
Split the Middle
Grouping
Factoring a monomial out
If a quadratic equation does not factor we can solve it by two different methods
1.) Completing the Square (today’s lesson)
2.) Quadratic Formula (Thursday)
That leaves us 5 ways to solve. There are a lot of ways to get your answer. Don’t give up.

3. 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

4. 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

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

6. 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 =0 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 4/2= 2²=4 3.) Add the number you got to complete the square to both sides of the equation Ex: x² -4x +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

7. Solve by Completing the Square+9

8. Solve by Completing the Square
+121

9. Solve by Completing the Square+1

10. Solve by Completing the Square
+25

11. Solve by Completing the Square
+16

12. Solve by Completing the Square+9

13. The coefficient of x2 must be “1”

14. The coefficient of x2 must be “1”

16. Solving Quadratic Equations by Completing the Square
Solve the following equation by completing the square:
Step 1: Move quadratic term, and linear term to left side of the equation

17. Solving Quadratic Equations by Completing the Square
Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

18. Solving Quadratic Equations by Completing the Square
Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

19. Solving Quadratic Equations by Completing the Square
Step 4: Take the square root of each side

20. Solving Quadratic Equations by Completing the Square
Step 5: Set up the two possibilities and solve