Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find the value of c such that each expression is a perfect-square trinomial.

7. x 2 + 18 x + c x squared , plus 18 . x plus c
8. z 2 + 22 z + c z squared , plus 22 . z plus c
9. p 2 − 30 p + c p squared , minus 30 . p plus c
10. k 2 − 5 k + c k squared , minus 5 . k plus c
11. g 2 + 17 g + c g squared , plus 17 . g plus c
12. q 2 − 4 q + c q squared , minus 4 . q plus c

See Problems 2 and 3.

Solve each equation by completing the square. If necessary, round to the nearest hundredth.

13. g 2 + 7 g = 144 g squared , plus 7 . g equals 144
14. r 2 − 4 r = 30 r squared , minus 4 . r equals 30
15. m 2 + 16 m = − 59 m squared , plus 16 . m equals negative 59
16. q 2 + 4 q = 16 q squared , plus 4 . q equals 16
17. x 2 + 18 x = 307 x squared , plus 18 . x equals 307
18. z 2 − 2 z = 323 z squared , minus 2 . z equals 323
19. a 2 − 2 a − 35 = 0 eh squared , minus 2 . eh minus 35 equals 0
20. m 2 + 12 m + 19 = 0 m squared , plus 12 . m plus 19 equals 0
21. w 2 − 14 w + 13 = 0 w squared , minus 14 . w plus 13 equals 0
22. p 2 + 5 p − 7 = 0 p squared , plus 5 . p minus 7 equals 0
23. t 2 + t − 28 = 0 t squared , plus , t minus 28 equals 0
24. g 2 + 11 g − 468 = 0 g squared , plus 11 . g minus 468 equals 0

See Problem 4.

Solve each equation by completing the square. If necessary, round to the nearest hundredth.

25. 4 a 2 − 8 a = 24 4 eh squared , minus 8 eh equals 24
26. 2 y 2 − 8 y − 10 = 0 2 y squared , minus 8 y minus 10 equals 0
27. 5 n 2 − 3 n − 15 = 10 5 n squared , minus 3 n minus 15 equals 10
28. 4 w 2 + 12 w − 44 = 0 4 w squared , plus 12 w minus 44 equals 0
29. 3 r 2 + 18 r = 21 3 r squared , plus 18 r equals 21
30. 2 v 2 − 10 v − 20 = 8 2 v squared , minus 10 v minus 20 equals 8

31. Art The painting shown below has an area of 420  in. 2 . 420 . in. squared , .  What is the value of x?

    

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