132 Chapter 1 Equations and Inequalities 43. (2x + 1)2 = 27 44. (5y + 2)? - 48 = 0 77. 3x2 = - 5x 1 78. 2x = 5x + 11 45. (5x + 1)2 = -8 46. (7y + 2)2 + 48 = 0 79. x + 1 = -7x 80. 13x + 1 = -10x 81. 3x + 6x = -1 82. 2x(x + 3) = -1 Complete the square to make each a perfect-square trinomial. 47. x2 + 6x 48. x? + 8x 83. 7x = 2x + 2 84. 5x x + = 3 49. x - 4x 50. x – 12x 85. x + 2x + 2 = 0 86. a + 4a + 8 = 0 51. a + 5a 52. 12 + 9t 87. y + 4y + 5 = 0 88. x² + 2x + 5 = 0 53. 7 - 11r 54. s? - 7s 89. x2 - 2x = -5 90. z2 – 3z = -8 3 55. y + 3 56. p + p 2 2 x%3D 9 5 91. x - 92. x + = X 1 57. q - 2 58. m - " 59 Solve each formula for the indicated variable. 1 93. h = 28 Solve each equation by completing the square. 94. x² + y? = r; x 59. x + 12x = -8 60. x - 6x = -1 61. x - 10x + 37 = 0 62. a + 16a + 82 = 0 95. h = 641 – 161; t 96. y = 16x - 4; x 63. x² + 5 = -5x 64. x2 + 1 = -4x = 1; x b? 97. 98. 1; y b²
132 Chapter 1 Equations and Inequalities 43. (2x + 1)2 = 27 44. (5y + 2)? - 48 = 0 77. 3x2 = - 5x 1 78. 2x = 5x + 11 45. (5x + 1)2 = -8 46. (7y + 2)2 + 48 = 0 79. x + 1 = -7x 80. 13x + 1 = -10x 81. 3x + 6x = -1 82. 2x(x + 3) = -1 Complete the square to make each a perfect-square trinomial. 47. x2 + 6x 48. x? + 8x 83. 7x = 2x + 2 84. 5x x + = 3 49. x - 4x 50. x – 12x 85. x + 2x + 2 = 0 86. a + 4a + 8 = 0 51. a + 5a 52. 12 + 9t 87. y + 4y + 5 = 0 88. x² + 2x + 5 = 0 53. 7 - 11r 54. s? - 7s 89. x2 - 2x = -5 90. z2 – 3z = -8 3 55. y + 3 56. p + p 2 2 x%3D 9 5 91. x - 92. x + = X 1 57. q - 2 58. m - " 59 Solve each formula for the indicated variable. 1 93. h = 28 Solve each equation by completing the square. 94. x² + y? = r; x 59. x + 12x = -8 60. x - 6x = -1 61. x - 10x + 37 = 0 62. a + 16a + 82 = 0 95. h = 641 – 161; t 96. y = 16x - 4; x 63. x² + 5 = -5x 64. x2 + 1 = -4x = 1; x b? 97. 98. 1; y b²
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
For number 95, how did they get an 8?

Transcribed Image Text:146 of 898
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132 Chapter 1 Equations and Inequalities
43. (2x + 1)² = 27
44. (5y + 2)² – 48 = 0
77. 3x2 = - 5x – 1
78. 2x2 = 5x + 11
45. (5x + 1)² = -8
46. (7y + 2)² + 48 = 0
79. x² + 1 = -7x
80. 13x2 + 1 = - 10x
81. 3x + 6x = - 1
82. 2x(x + 3) = –1
Complete the square to make each a perfect-square
trinomial.
47. x² + 6x
48. x² + 8x
83. 7x = 2x + 2
84. 5x x +
= 3
49. х2 — 4х
50. х2
12x
85. x + 2x + 2 = 0
86. a? + 4a + 8 = 0
51. a + 5a
52. 12 + 9t
87. y + 4y + 5 = 0
88. x² + 2x + 5 = 0
53. 2 — 11г
54. s² – 7.s
89. x2 – 2x = - 5
90. z2 – 3z = -8
3
55. y +
3
56. р? +
2
91. x² -
3
2
92. x? +
4
1
57. q - 34
2
58. т?
m
Solve each formula for the indicated variable.
Solve each equation by completing the square.
1
93. h =
94. x² + y? = r²; x
59. x + 12x = -8
60. x² – 6x = -1
61. х.
10x + 37 = 0
62. a + 16a + 82 = 0
95. h = 64t – 167²; t
96. у %3
16x2 – 4; x
63. x² + 5 = -5x
64. x² + 1 = -4x
97.
1; у
98.
a
= 1; x
%3D
65. y + 11y = -49
66. x² – 5x = -22
99.
a?
1; а
100.
a?
1; b
b²
67. 2x2 – 20x = -49
68. 4x2 + 8x = 7
69. 3x² = 1 – 4x
70. 3x2 + 4x = 5
101. х2 + ху — у? %3D 0;B х
71. 2x² = 3x + 1
72. 2x2 + 5x = 14
102. х? — 3ху + у' %3D0; у
Use the discriminant to determine the number and type of
roots. Do not solve the equation.
Use the Quadratic Formula to solve each equation.
74. 7z2 = –14z – 13
103. x + 6x + 9 = 0
104. -3x2 + 2x = 21
73. 9х?
18x – 14
105. 3x2 – 2x + 5 = 0
106. 9x² + 42.x + 49 = 0
75. 2x2 = 14x –
30i
76. 5x² + x = -5
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right
o remove additional content at any time if subsequent rights restrictions require it.

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Expert Solution & Answer
Answer to Problem 95E
8±/64–h
The formula for t is t =
4
Explanation of Solution
Quadratic Formula:
-b±/b² -4ac
The solutions of the general quadratic equation, ax? + bx + c = 0, are x =
(a + 0).
2a
Calculation:
The given equation can be rewritten as 1612 – 64t + h = 0.
Solve 16t2 – 64t + h = 0 for t by using Quadratic formula as follows.
Here, a =
= 16, b
= -64 and c = h.
Substitute these values in the Quadratic Formula as,
-b ± /b? – 4ac
t =
2a
- (-64) ±
(-64)² – 4 (16) (h)
2 (16)
64 + V-64h + 4096
How?
2 (16)
64
8-h + 64
32
8 ± V64 – h
8±/64-h
Therefore, the formula for t is t =
Final statement:
8±/64-h
The formula for t is t =
4
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Chapter 1.4, Problem 96E
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