Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each equation by finding square roots.

12. 5 x 2 = 80 5 x squared , equals 80
13. x 2 − 4 = 0 x squared , minus 4 equals 0
14. 2 x 2 = 32 2 x squared , equals 32
15. 9 x 2 = 25 9 x squared , equals 25
16. 3 x 2 − 15 = 0 3 x squared , minus 15 equals 0
17. 5 x 2 − 40 = 0 5 x squared , minus 40 equals 0

See Problem 2.

18. Fitness A rectangular swimming pool is 6 ft deep. One side of the pool is 2.5 times longer than the other. The amount of water needed to fill the swimming pool is 2160 cubic feet. Find the dimensions of the pool.

See Problem 3.

Solve each equation.

19. x 2 + 6 x + 9 = 1 x squared , plus 6 x plus 9 equals 1
20. x 2 − 4 x + 4 = 100 x squared , minus 4 x plus 4 equals 100
21. x 2 − 2 x + 1 = 4 x squared , minus 2 x plus 1 equals 4
22. x 2 + 8 x + 16 = 16 9 x squared , plus 8 x plus 16 equals , 16 over 9
23. 4 x 2 + 4 x + 1 = 49 4 x squared , plus 4 x plus 1 equals 49
24. x 2 − 12 x + 36 = 25 x squared , minus 12 x plus 36 equals 25
25. 25 x 2 + 10 x + 1 = 9 25 x squared , plus 10 x plus 1 equals 9
26. x 2 − 30 x + 225 = 400 x squared , minus 30 x plus 225 equals 400
27. 9 x 2 + 24 x + 16 = 36 9 x squared , plus 24 x plus 16 equals 36

See Problem 4.

Complete the square.

28. x 2 + 18 x + □ x squared , plus 18 x plus white square
29. x 2 − x + □ x squared , minus x plus white square
30. x 2 − 24 x + □ x squared , minus 24 x plus white square
31. x 2 + 20 x + □ x squared , plus 20 x plus white square
32. m 2 − 3 m + □ m squared , minus 3 m plus white square
33. x 2 + 4 x + □ x squared , plus 4 x plus white square

See Problem 5.

Solve each quadratic equation by completing the square.

34. x 2 + 6 x − 3 = 0 x squared , plus 6 x minus 3 equals 0
35. x 2 − 12 x + 7 = 0 x squared , minus 12 x plus 7 equals 0
36. x 2 + 4 x + 2 = 0 x squared , plus 4 x plus 2 equals 0
37. x 2 − 2 x = 5 x squared , minus 2 x equals 5
38. x 2 + 8 x = 11 x squared , plus 8 x equals 11
39. x 2 + 12 = 10 x x squared , plus 12 equals 10 x
40. x 2 − 3 x = x − 1 x squared , minus 3 x equals x minus 1
41. x 2 + 2 = 6 x + x squared , plus 2 equals 6 x plus  4
42. 2 x 2 + 2 x − 5 = x 2 2 x squared , plus 2 x minus 5 equals , x squared
43. 4 x 2 + 10 x − 3 = 0 4 x squared , plus 10 x minus 3 equals 0
44. 9 x 2 − 12 x − 2 = 0 9 x squared , minus 12 x minus 2 equals 0
45. 25 x 2 + 30 x = 12 25 x squared , plus 30 x equals 12

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