8 to solve 2 x x 2 0 by the quadratic formula let a 1

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8. To solve 2 x x 2 0 by the quadratic formula, let a 1, b 2, and c 0. 9. Two numbers that have a sum of 6 can be represented by x and x 6. 10. Some quadratic equations have one real and one imaginary solution. e e 2 4 df 2 d dug22241_ch10a.qxd 11/10/2004 18:30 Page 635

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10-21 10.2 The Quadratic Formula 637 51. 3 y 2 2 y 4 0 52. 2 y 2 3 y 6 0 53. w w 2 w w 3 54. 3 y y 4 y 2 4 55. 9(3 x 4 5) 2 1 56. 25(2 x 9 1) 2 0 57. 25 1 3 x 2 0 58. 4 2 9 1 4 x 2 0 59. 1 2 x 0 2 8 x 60. 3 x 4 2 6 x 1 61. ( x 8)( x 4) 42 62. ( x 10)( x 2) 20 63. y 3 8 ( ( 2 y y 1 5 ) ) 64. z 12 7 ( z z 4 1) Use the quadratic formula and a calculator to solve each equation. Round answers to three decimal places and check your answers. 65. x 2 3.2 x 5.7 0 66. x 2 7.15 x 3.24 0 67. x 2 7.4 x 13.69 0 68. 1.44 x 2 5.52 x 5.29 0 69. 1.85 x 2 6.72 x 3.6 0 70. 3.67 x 2 4.35 x 2.13 0 71. 3 x 2 14,379 x 243 0 72. x 2 12,347 x 6741 0 73. x 2 0.00075 x 0.0062 0 74. 4.3 x 2 9.86 x 3.75 0 Find the exact solution(s) to each problem. If the solution(s) are irrational, then also find approximate solution(s) to the nearest tenth. See Example 6. 75. Missing numbers. Find two positive real numbers that differ by 1 and have a product of 16. 76. Missing numbers. Find two positive real numbers that differ by 2 and have a product of 10.

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