Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution.

8. x 2 − 9 = 0 x squared , minus 9 equals 0
9. x 2 + 7 = 0 x squared , plus 7 equals 0
10. 3 x 2 = 0 3 x squared , equals 0
11. 3 x 2 − 12 = 0 3 x squared , minus 12 equals 0
12. x 2 + 4 = 0 x squared , plus 4 equals 0
13. 1 3 x 2 − 3 = 0 1 third , x squared , minus 3 equals 0
14. 1 2 x 2 + 1 = 0 1 half , x squared , plus 1 equals 0
15. x 2 + 5 = 5 x squared , plus 5 equals 5
16. 1 4 x 2 + 1 = 0 1 fourth , x squared , plus 1 equals 0
17. x 2 + 25 = 0 x squared , plus 25 equals 0
18. x 2 − 10 = − 10 x squared , minus 10 equals . minus 10
19. 2 x 2 − 18 = 0 2 x squared , minus 18 equals 0

See Problem 2.

Solve each equation by finding square roots. If the equation has no real-number solution, write no solution.

20. n 2 = 81 n squared , equals 81
21. a 2 = 324 eh squared , equals 324
22. k 2 − 196 = 0 k squared , minus 196 equals 0
23. r 2 + 49 = 49 r squared , plus 49 equals 49
24. w 2 − 36 = − 64 w squared , minus 36 equals . minus 64
25. 4 g 2 = 25 4 g squared , equals 25
26. 64 b 2 = 16 64 b squared , equals 16
27. 5 q 2 − 20 = 0 5 q squared , minus 20 equals 0
28. 144 − p 2 = 0 144 minus . p squared , equals 0
29. 2 r 2 − 32 = 0 2 r squared , minus 32 equals 0
30. 3 a 2 + 12 = 0 3 eh squared , plus 12 equals 0
31. 5 z 2 − 45 = 0 5 z squared , minus 45 equals 0

See Problem 3.

Model each problem with a quadratic equation. Then solve. If necessary, round to the nearest tenth.

32. Find the length of a side of a square with an area of 169  m 2 . 169 , m squared , .
33. Find the length of a side of a square with an area of 75  ft  2 . 75 , ft squared , .
34. Find the radius of a circle with an area of 90  cm  2 . 90 , cm squared , .
35. Painting You have enough paint to cover an area of 50  ft  2 . 50 , ft squared , .  What is the side length of the largest square that you could paint? Round your answer to the nearest tenth of a foot.
36. Gardening You have enough shrubs to cover an area of 100  ft  2 . 100 . ft squared , .  What is the radius of the largest circular region you can plant with these shrubs? Round your answer to the nearest tenth of a foot.

B Apply

Mental Math Tell how many solutions each equation has.

37. h 2 = − 49 h squared , equals , minus 49
38. c 2 − 18 = 9 c squared , minus 18 equals 9
39. s 2 − 35 = − 35 s squared , minus 35 equals . minus 35

40. Think About a Plan A circular above-ground pool has a height of 52 in. and a volume of 1100  ft  3 . 1100 . ft cubed , .  What is the radius of the pool to the nearest tenth of a foot? Use the equation V = π r 2 h , v equals pi , r squared , h comma  where V is the volume, r is the radius, and h is the height.

    • How can drawing a diagram help you solve this problem?
    • Do you need to convert any of the given measurements to different units?
41. Reasoning For what values of n will the equation x 2 = n x squared , equals , n  have two solutions? Exactly one solution? No solution?

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