Completing the Square pages 544–546 Exercises 12. 19, –17 24. 7, –2 ALGEBRA 1 LESSON 10-6 pages 544–546  Exercises 1. 49 2. 16 3. 400 4. 9 5. 144 6. 324 7. 4, –12 8. 13.06, –3.06 9. –5, –17 10. 1.24, –7.24 11. 9, –29 12. 19, –17 13. 7, –5 14. –2.17, –7.83 15. 11, 1 16. 1.19, –4.19 17. 4.82, –5.82 18. 22, –31 19. 1 20. 4 21. 22. 2.16, –4.16 23. 5, –1 24. 7, –2 25. a. (2x + 1)(x + 1) b. 2x2 + 3x + 1 = 28 c. 3 26. –0.27, –3.73 27. –3, –4 28. 4, –10 29. 6, 2 30. 8.32, 1.68 31. no solution 32. 9.37, –1.87 33. 8.12, –0.12 34. –4, –5 81 100 10-6

d. No; the answers in part (b) were rounded. Completing the Square ALGEBRA 1 LESSON 10-6 35. a. = 50 – 2w b. w(50 – 2w) = 150; 21.5, 3.5 c. 7 ft  21.5 ft or 43 ft  3.5 ft d. No; the answers in part (b) were rounded. 36. The student did not divide each side of the equation by 4. 37. Answers may vary. Sample: Add 1 to each side of the equation, and then complete the square by adding 225 to each side of the equation. Write x2 + 30x + 225 as the square (x + 15)2 and add 1 and 225 to get 226. Then take square roots and solve the resulting equations. 38. Answers may vary. Sample: x2 + 10x – 50 = 0 x2 + 10x = 50 x2 + 10x + 25 = 50 + 25 (x + 5)2 = ± 75 x + 5 = ± 8.7 x + 5 ± 8.7 x + 5 8.7 or x + 5 –8.7 x 3.7  or  x –13.7 39. 5.16, –1.16 40. 6.83, 1.17 41. 5.6 ft by 14.2 ft 42. a. 6x2 + 28x b. 6x2 + 28x = 384 c. 13 in.  6 in.  6 in. 10-6

The value of x is about 13.18 cm. [1] appropriate methods, Completing the Square ALGEBRA 1 LESSON 10-6 43. a. A = x2 + 5x + 1 b. 6.86 c. 207.5 ft2 44. a. 3 ± 5 b. (3, –5) c. Answers may vary. Sample: p is the x-coordinate of the vertex. 45. B 46. I 47. D 7 2 48. [2] (x)(x + x + 4) = 200 (x)(2x + 4) = 200 (x)(x + 2) = 200 x2 + 2x = 200 x2 + 2x + 1 = 201 (x + 1)2 = 201 x + 1 ±14.18 x 13.18   x –15.18 The value of x is about 13.18 cm. [1] appropriate methods, but with one computational error 1 2 1 2 10-6

[3] appropriate methods, but with one computational error Completing the Square ALGEBRA 1 LESSON 10-6 53. – , 54. – 55. – , 56. (x + 2)2 57. (t – 11)2 58. (b + 5)(b – 5) 59. (4c + 3)2 60. (7s + 13)(7s – 13) 61. 2m(2m + 3)(2m – 3) 62. (5m + 12)2 63. (20k + 3)(20k – 3) 64. (16g – 11)(16g + 11) 8 3 8 3 65. r 12 66. p13 67. –y 68. 69. – 70. t 29 49. [4] a. (8 + x)(12 + x) = 2 • (8 • 12) x2 + 20x – 96 = 0 b. x2 + 20x = 96 x2 + 20x + 100 = 196 (x + 10)2 = 196 x + 10 = ±14 x = 4 c. 12 ft by 16 ft [3] appropriate methods, but with one computational error [2] part (c) not done [1] no work shown 50. –3, 7 51. –6, –5 52. 0, 5 3 2 1 6 5 2 1 m40 1 w 10-6