140 CHAPTER 1 Equations and Inequalities Solve each equation using the quadratic formula. See Examples 5 and 6. 51. x2 - x - 1 = 0 52. x2 - 3x - 2 = 0 53. x2 - 6x = -7 54. x2 - 4x = -1 55. x2 = 2x - 5 56. x2 = 2x - 10 57. -4x2 = -12x + 11 58. -6x2 = 3x + 2 59. 1 2 x2 + 1 4 x - 3 = 0 60. 2 3 x2 + 1 4 x = 3 61. 0.2x2 + 0.4x - 0.3 = 0 62. 0.1x2 - 0.1x = 0.3 63. 14x - 121x + 22 = 4x 64. 13x + 221x - 12 = 3x 65. 1x - 921x - 1 = -16 66. Concept Check Why do the following two equations have the same solution set? (Do not solve.) -2x2 + 3x - 6 = 0 and 2x2 - 3x + 6 = 0 50. Francesca claimed that the equation x2 - 19 = 0 cannot be solved by the quadratic formula since there is no value for b. Is she correct? Solve each cubic equation using factoring and the quadratic formula. See Example 7. 67. x3 - 8 = 0 68. x3 - 27 = 0 69. x3 + 27 = 0 70. x3 + 64 = 0 Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. 71. s = 1 2 gt2, for t 72. = pr2, for r 73. F = kMv2 r , for v 74. E = e2k 2r , for e 75. r = r0 + 1 2 at2, for t 76. s = s 0 + gt 2 + k, for t 77. h = -16t2 + v 0t + s0, for t 78. S = 2prh + 2pr 2, for r For each equation, (a) solve for x in terms of y, and (b) solve for y in terms of x. See Example 8. 79. 4x2 - 2xy + 3y2 = 2 80. 3y2 + 4xy - 9x2 = -1 81. 2x2 + 4xy - 3y2 = 2 82. 5x2 - 6xy + 2y2 = 1 Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9. 83. x2 - 8x + 16 = 0 84. x2 + 4x + 4 = 0 85. 3x2 + 5x + 2 = 0 86. 8x2 = -14x - 3 87. 4x2 = -6x + 3 88. 2x2 + 4x + 1 = 0 89. 9x2 + 11x + 4 = 0 90. 3x2 = 4x - 5 91. 8x2 - 72 = 0
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