Solutions

Solutions to Try Its

1. (x−6)(x+1)=0;x=6,x=−1(x−6)(x+1)=0;x=6,x=−1

2. (x−7)(x+3)=0(x−7)(x+3)=0, x=7x=7, x=−3x=−3.

3. (x+5)(x−5)=0(x+5)(x−5)=0, x=−5x=−5, x=5x=5.

4. (3x+2)(4x+1)=0(3x+2)(4x+1)=0, x=−23x=−23, x=−14x=−14

5. x=0,x=−10,x=−1x=0,x=−10,x=−1

6. x=4±√5x=4±√5

7. x=3±√22x=3±√22

8. x=−23x=−23, x=13x=13

9. 55 units

Solutions to Odd-Numbered Exercises

1. It is a second-degree equation (the highest variable exponent is 2).

3. We want to take advantage of the zero property of multiplication in the fact that if a⋅b=0a⋅b=0 then it must follow that each factor separately offers a solution to the product being zero: a=0 or b=0a=0 or b=0.

5. One, when no linear term is present (no x term), such as x2=16x2=16. Two, when the equation is already in the form (ax+b)2=d(ax+b)2=d.

7. x=6x=6, x=3x=3

9. x=−52x=−52, x=−13x=−13

11. x=5x=5, x=−5x=−5

13. x=−32x=−32, x=32x=32

15. x=−2x=−2

17. x=0x=0, x=−37x=−37

19. x=−6x=−6, x=6x=6

21. x=6x=6, x=−4x=−4

23. x=1x=1, x=−2x=−2

25. x=−2x=−2, x=11x=11

27. x=3±√22x=3±√22

29. z=23, z=−12

31. x=3±√174

33. Not real

35. One rational

37. Two real; rational

39. x=−1±√172

41. x=5±√136

43. x=−1±√178

45. x≈0.131 and x≈2.535

47. x≈−6.7 and x≈1.7

49. ax2+bx+c=0x2+bax=−cax2+bax+b24a2=−ca+b4a2(x+b2a)2=b2−4ac4a2x+b2a=±√b2−4ac4a2x=−b±√b2−4ac2a

51. x(x+10)=119; 7 ft. and 17 ft.

53. maximum at x=70

55. The quadratic equation would be (100x−0.5x2)−(60x+300)=300. The two values of x are 20 and 60.

57. 3 feet