Solving Equations Using Factoring

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.

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

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.

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

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

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?

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

Set each factor equal to zero 2w + 15 = 0 w – 6 = 0 Solve: w = -7.5 w = 6 The width cannot be negative so it cannot be -7.5. It must be 6 feet. The length is 3 more than twice 6 Dimensions are 6 feet by 15 feet

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

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