1. Solving Equations Using Factoring

2. Quadratic Equations
A quadratic equation is an equation that can be written in the standard form: ax² + bx + c = 0
Quadratic equations will have zero, one, or two solutions.

3. Ways to Solve Quadratic Equations
Graphing
Factoring
Square Root Method
3x2 = 108
Quadratic Formula
3x2 – 2x + 3 = 0
Completing the Square

4. Solving by Factoring x2 + 5x = -6 Make it equal zero x2 + 5x + 6 = 0
Factor the left side (use the box or one of the short cuts).
(x + 2)(x + 3) = 0
Set ALL FACTORS (including both sets of parentheses) equal to zero.

5. Solving by Factoring (cont.)
x + 2 = 0 x + 3 = 0
Solve.
x = -2 and x = -3

6. Example 2 x3 + x2 – 6x = 0 Factor: x(x2 + x – 6) = 0
Set each factor equal to zero:
x = 0 x – 2 = 0 x + 3 = 0
Solve:
x = 0, 2, -3

7. Word Problem
You are building a rectangular wading pool. You want the area of the bottom to be 90 ft2. You want the length of the pool to be 3 ft longer than twice its width. What will be the dimensions of pool?

8. Word Problem (cont) Draw a picture. w(2w + 3) = 90 Distribute
Make it equal zero
2w2 + 3w – 90 = 0
Factor
(2w + 15)(w – 6) = 0 w
2w + 3

9. Set each factor equal to zero
2w + 15 = w – 6 = 0
Solve:
w = w = 6
The width cannot be negative so it cannot be It must be 6 feet.
The length is 3 more than twice 6
Dimensions are 6 feet by 15 feet

10. Try these… x2 + 11x + 30 = 0 x = -5, -6 2x2 – 5x = 88 x = -5.5, 8

11. Try these (cont)…
You are building a rectangular wading pool. You want the area of the bottom to be 105 ft2. You want the length of the pool to be 1 ft longer than twice its width. What will be the dimensions of pool?
7 feet by 15 feet