Solve each equation using any method. When necessary, round real solutions to the nearest hundredth.

41. 6 x 2 − 5 x − 1 = 0 6 x squared , minus 5 x minus 1 equals 0
42. 7 x 2 − x − 12 = 0 7 x squared , minus x minus 12 equals 0
43. 5 x 2 + 8 x − 11 = 0 5 x squared , plus 8 x minus 11 equals 0
44. 4 x 2 + 4 x = 22 4 x squared , plus 4 x equals 22
45. 2 x 2 − 1 = 5 x 2 x squared , minus 1 equals 5 x
46. 2 x 2 + x = 1 2 2 x squared , plus x equals , 1 half
47. x 2 = 11 x − 10 x squared , equals 11 x minus 10
48. 5 x 2 = 210 x 5 x squared , equals 210 x
49. 4 x 2 + 4 x = 3 4 x squared , plus 4 x equals 3
50. 2 x 2 + 4 x = 10 2 x squared , plus 4 x equals 10
51. x 2 − 3 x − 8 = 0 x squared , minus 3 x minus 8 equals 0
52. − 3 x 2 + 147 = 0 negative 3 , x squared , plus 147 equals 0
53. x 2 + 8 x = 4 x squared , plus 8 x equals 4
54. 4 x 2 − 4 x − 3 = 0 4 x squared , minus 4 x minus 3 equals 0
55. x 2 = 11 − 6 x x squared , equals 11 minus 6 x
56. Air Pollution The function y = 0 . 4409 x 2 − 5 . 1724 x + 99.0321 y equals 0 . , 4409 , x squared , minus 5 . , 1724 , x plus , 99.0321  models the emissions of carbon monoxide in the United States since 1987, where y represents the amount of carbon monoxide released in a year in millions of tons, and x = 0 x equals 0  represents the year 1987.
    1. How can you use a graph to estimate the year in which more than 100 million tons of carbon monoxide were released into the air?
    2. How can you use the Quadratic Formula to estimate the year in which more than 100 million tons of carbon monoxide were released into the air?
    3. Which method do you prefer? Explain why.
57. Sports A diver dives from a 10 m springboard. The equation f ( t ) = − 4 . 9 t 2 + 4 t + 10 f open t close equals negative 4 . 9 , t squared , plus 4 t plus 10  models her height above the pool at time t in seconds. At what time does she enter the water?

Without graphing, determine how many x-intercepts each function has.

58. y = − 2 x 2 + 3 x − 1 y equals negative 2 , x squared , plus 3 x minus 1
59. y = 0 . 25 x 2 + 2 x + 4 y equals 0 . 25 , x squared , plus 2 x plus 4
60. y = x 2 + 3 x + 5 y equals , x squared , plus 3 x plus 5
61. y = − x 2 + 3 x + 10 y equals negative , x squared , plus 3 x plus 10
62. y = 3 x 2 − 10 x + 6 y equals , 3 x squared , minus 10 x plus 6
63. y = 10 x 2 + 13 x − 3 y equals , 10 x squared , plus 13 x minus 3
64. y = x 2 + 17 x − 2 y equals , x squared , plus 17 x minus 2
65. y = − 5 x 2 − 4 x + 3 y equals negative 5 , x squared , minus 4 x plus 3
66. y = 7 x 2 − 2 x + 9 y equals , 7 x squared , minus 2 x plus 9
67. Reasoning Determine the value(s) of k for which 3 x 2 + k x + 12 = 0 3 x squared , plus k x plus 12 equals 0  has each type of solution.
    1. no real solutions
    2. exactly one real solution
    3. two real solutions
68. Use the discriminant to match each function with its graph.

    f ( x ) = x 2 − 4 x + 2 f open x close equals , x squared , minus 4 x plus 2 f ( x ) = x 2 − 4 x + 4 f open x close equals , x squared , minus 4 x plus 4 f ( x ) = x 2 − 4 x + 6 f open x close equals , x squared , minus 4 x plus 6

69. 1. Geometry Write an equation to find the dimensions of a square that has the same area as a circle with a radius of 10 cm.
    2. Find the length of a side of the square, to the nearest hundredth centimeter.

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