1. Squarely brought to you squares by
Completing the Square
Squarely brought to you squares by
Mr. Peter Richard
(Who is not a square)

2. Many quadratic equations contain expressions that cannot be easily factored. For equations containing these types of expressions, you can use square roots to find the roots.
Sometimes you may have to round the roots, so they are no longer square roots, they are rounded roots!

3. Perfect Square Trinomials
Examples
x2 + 6x + 9
x2 - 10x + 25
x2 + 12x + 36

4. 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.
(14/2)2
X2 + 14x + 49

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

6. 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

7. Solving Quadratic Equations by Completing the Square
Step 2: Take half of the middle (B) term. Square it, and add it
to both sides of the equal sign.

8. 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)(x+4) = 36
(x + 3)2 (
+ 3)(x + 3) or (x + 3)2

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

10. Solving Quadratic Equations by Completing the Square
Step 5: Solve both equations

11. To complete the square of the expression x2 + bx, add

12. Example. x2 – 8x
Add
x2 – 8x +
= (x – 4)2
= x2 – 8x + 16

13. Ex. x2 + 10x = 24
x2 + 10x = 24
Add to both
sides
x2 + 10x + 25 = 49
Find the square root
of both sides
(x + 5)2 = 49
x + 5 =
x = 2 or x = -12

14. Ex. x2 – 2x – 3 = 0 x² - 2x = 3 x² -2x + = 3 + (x – 1)² = 4 X – 1 = ±2
X = 3 or -1

15. Ex: 2x² + 7x + 3 = 0
Do this one yourself so that you know that I know that you know how to do it!

16. Quiz & Homework Quiz: Page 285 # 2, 4, 6, 14, 17