1. 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
, –3.06
9. –5, –17
, –7.24
11. 9, –29
12. 19, –17
13. 7, –5
14. –2.17, –7.83
15. 11, 1
, –4.19
, –5.82
18. 22, –31
19. 1
20. 4
21.
, –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
, 1.68
31. no solution
, –1.87
, –0.12
34. –4, –5 81
100
10-6

2. 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 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 =
(x + 5)2 = ± 75
x + 5 = ± 8.7
x ± 8.7
x or x –8.7
x   or  x –13.7
, –1.16
, 1.17
ft by 14.2 ft
42. a. 6x2 + 28x
b. 6x2 + 28x = 384
c. 13 in.  6 in.  6 in.
10-6

3. 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 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 ±14.18
x    x –15.18
The value of x is about cm.
[1] appropriate methods,
but with one computational error 1 2 1 2
10-6

4. [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 = 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