5.2.3 Solving Quadratic Equations by Factoring

Problems 92-94 Solutions

92. 1. area: 40

length: x + 3

width: x

2. (x + 3)(x) = 40

3. (x + 3)(x) = 40

x² + 3x = 40

x² + 3x – 40 = 0

(x – 5)(x + 8) = 0

x – 5 = 0 or x + 8 = 0

x = 5 or x = -8

4. x = 5 or x = 8 ?

5. x = 5

93. 1, area: 105

length: 2x + 1

width: x

2. (2x + 1)(x) = 105

3. (2x + 1)(x) = 105

2x2 + x = 105

2x2 + x – 105 = 0

(2x + 15)(x – 7) = 0

2x + 15 = 0 or x – 7 = 0

2x = -15

x = -7½ or x = 7

4. x = -7½ or x = 7

5. x = 7

94. 1. area: 22

length: 3x – 1

height: x

2. (3x – 1)(x) = 22

3. (3x – 1)(x) = 22

2(3x – 1)(x) = 22 · 2

2

(3x – 1)(x) = 44

3x2 – x = 44

3x2 – x – 44 = 0

(3x + 11)(x - 4) = 0

3x + 11 = 0 or x - 4 = 0

3x = -11

x = -3²/₃ or x = 4

4. x = -3²/₃ or x = 4

5. x = 4