1. Solving Quadratic Equations by Completing the Square

2. Perfect Square Trinomials
Examples
a2 + 2ab + b2
a2 – 2ab + b2
x2 + 6x + 9
x2 - 10x + 25
x2 + 12x + 36

3. Creating a Perfect Square Trinomial
In the following perfect square trinomial, the constant term is missing x2 + 14x + ____
Find the constant term by squaring half the coefficient of the linear term.
x2 + 14x + 49

4. Perfect Square Trinomials
Create perfect square trinomials.
x2 + 20x + ___
x2 - 4x + ___
x2 + 5x + ___
100 4
25 4

5. 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

6. 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.

7. 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.
𝒙+𝟒 𝟐 =𝟑𝟔

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

9. Solving Quadratic Equations by Completing the Square
Step 5: Set up the two possibilities and solve.
x = –4 ± 6
x = –4 – 6 or x = –4 + 6
x = –10 or x = 2

10. Completing the Square-Example #2
Solve the following equation by completing the square:
Step 1: Move quadratic term, and linear term to left side of the equation, the constant to the right side of the equation.

11. 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.
The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first.

12. 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.

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

14. Solving Quadratic Equations by Completing the Square
Try the following examples. Do your work on your paper and then check your answers.
x = –9 or x = 7
x = –14 or x = 6
x = –3 or x = 8
x = −7 ± 𝑖 3 2
x = −5 ± 𝑖

15. Solve x2 + 2x – 63 = 0 x2 + 2x – 63 = 0 x2 + 2x + _____ = 63 + _____ 1
𝑥 = ± 8
x = 7 OR
x = –9
x + 1 = ± 8