## Destinyyyy one year ago Help with 5 problems...

1. Destinyyyy

2 [7- 3/2x] +5=21 [] are absolute value lines

2. Destinyyyy

7- 3/2x =8

3. Destinyyyy

Not sure what to do next

4. Destinyyyy

@Nnesha @freckles @Vocaloid

5. Vocaloid

you're on the right track, but when we have absolute value signs, we must consider the positive and negative solutions to the equation so, going by what you have so far, we have: | 7 - 3/2x | = 8, where | | are the absolute value signs, with me so far?

6. Destinyyyy

Yes

7. Vocaloid

So, going from there, we need to write two different equations 7 - 3/2x = 8 and 7 - 3/2x = -8

8. Vocaloid

then we solve each one separately so, let's tackle the first one 7 - 3/2x = 8 first, subtract 7 from both sides and tell me what you get

9. Destinyyyy

- 3/2x= 1

10. Vocaloid

yup, now we divide both sides by (-3/2)

11. Destinyyyy

um -2/3

12. Vocaloid

yup, so x = -2/3 now, we're only halfway done, there's another value of x that works for the equation. now we solve 7 - (3/2)x = -8 using the same process as before. start by subtracting 7 from both sides

13. Destinyyyy

x=10

14. Vocaloid

yup, so x = 10 and x = -2/3 are your two solutions, good work ready for the next one?

15. Destinyyyy

Yes thank you

16. Destinyyyy

Solve. [x+8] +9=7 same as the one before

17. Destinyyyy

I got x=-10

18. Vocaloid

ah, not quite, there's an important rule to remember when it comes to absolute values. the absolute value of a mathematical expression cannot be negative as an example, if we have |x| = a, then a must be a positive number in order to have a solution so, looking at our problem, we first subtract 9 from each side to get |x + 8| = -2 the absolute value of any quantity must be positive, so this has no solution

19. Destinyyyy

Okay

20. Vocaloid

does that make sense? are you ready to move to the next one?

21. Destinyyyy

Yes it does. I thought it was but wanted to make sure.. Solve using appropriate substitution. (x^2 -6x)^2 -11(x^2 -6x) -30=0

22. Destinyyyy

I got 3+- square root 14 and 3+- square root 15 But its wrong...

23. Vocaloid

huh, this is a tricky one, hold on a moment

24. Destinyyyy

Okay

25. Vocaloid

well, I'm not sure if this is the right approach but...I'm guessing it wants us to substitute a variable for x^2 -6x so, if we let a = x^2 -6x, then our equation becomes a^2 - 11a - 30 after we apply the quadratic formula we get |dw:1440800955390:dw|

26. Destinyyyy

I factored (w-5)(w-6)

27. Vocaloid

I'm not really sure if my thinking is correct and that factoring doesn't work, that would only work for positive 30, not -30 (w-5)(w-6) = w^2 - 11w + 30

28. Destinyyyy

Oops

29. Vocaloid

ah, I wish I could be of more help on this one :( I feel like I'm missing an obvious trick here @welshfella @SithsAndGiggles

30. Destinyyyy

31. anonymous

Given that $$a^2 - 11a - 30=0$$ yields roots $$a=\dfrac{11\pm\sqrt{241}}{2}$$, you can find the roots to $$x^2-x-a=0$$ by applying the QF again.

32. anonymous

typo: $$x^2-\color{red}6x-a=0$$

33. Destinyyyy

Um okay..

34. dinamix

w(1) = 5 or w(2) = 6

35. Destinyyyy

So... 1+- square root 5 over 2

36. dinamix

2 solution w(1) = 5 and w(2) = 6

37. dinamix

@Destinyyyy

38. Destinyyyy

Okay but how did you get to that?? Id like to know how to solve this

39. dinamix

$\Delta = 1$

40. dinamix

u should find that

41. Destinyyyy

The triangle is square root correct?

42. Destinyyyy

What?? O.o

43. dinamix

$w =\frac{ 11 \pm \sqrt{121-120} }{ 2}$

44. Destinyyyy

Yes I have that

45. Destinyyyy

Except I have a positive 120

46. Destinyyyy

121+120=241

47. Destinyyyy

Now what?

48. dinamix

u have mistake

49. Destinyyyy

Where?

50. dinamix

b^2-4ac = $(-11^2) - 4*1*30$

51. dinamix

u looking for this w^2-11w+30 @Destinyyyy

52. Destinyyyy

its a negative 30 not positive...

53. Destinyyyy

The original problem contains a -30

54. dinamix

what is your problem could u tell me what is equation

55. dinamix

plz

56. Destinyyyy

Solve using appropriate substitution. (x^2 -6x)^2 -11(x^2 -6x) -30=0

57. Destinyyyy

w^2 -11w -30=0 w^2--> (x^2-6x)^2 w--> x^2 -6x

58. dinamix

are u sure its -30 ? cuz like that we dont have good numbers

59. Destinyyyy

Its actually -80 ... I miss read. So sorry

60. Destinyyyy

Everything else is correct

61. dinamix

so give me right equation without mistakes

62. dinamix

ok

63. Destinyyyy

Solve using appropriate substitution. (x^2 -6x)^2 -11(x^2 -6x) -80=0 I can screenshot it if you want

64. dinamix

ok so w(1) = 5 and w(2) = 16

65. Destinyyyy

??

66. dinamix

i solve it when i do w^2-11w-80=0

67. dinamix

we have 2 solution w(1) = -5 and w(2) = 16

68. dinamix

u have too check it cuz i am sure about it

69. dinamix

@Destinyyyy did find like that or no ?

70. dinamix

$\frac{ 11\pm \sqrt{121+320} }{ 2 }$

71. Destinyyyy

I havent read a thing youve said... x= 5,1 x=-2,8

72. Destinyyyy

Correct?

73. Destinyyyy

I factored

74. Destinyyyy

???

75. dinamix

u have 2 find 6 nomber to solve this problem 8;-2;5;1;16;-5

76. Destinyyyy

Why 6 numbers?

77. Destinyyyy

The last one I did like this was 2 numbers

78. Destinyyyy

I dont count the w only the x's

79. Destinyyyy

x= 5,-2,8 I should have one more step

80. Destinyyyy

@jim_thompson5910

81. dinamix

w^2-11w-80 = 0 i find 2 numbers is -5 and 16 this only solution of W w----> x^2-6x we have find x now w=16 and w=x^2-6x------> x^2-6x=16 and also for -5 we solve this equation x^2-6x-16=0 and x^2-6x+5=0 and we find x

82. Destinyyyy

83. Destinyyyy

x= 5 and 1 x= -2 and 8

84. Destinyyyy

I should have another step where I do x^2

85. dinamix

yup this

86. dinamix

did u understand now

87. Destinyyyy

88. dinamix

yup u right

89. Destinyyyy

And there are no more steps?

90. dinamix

yeah

91. Destinyyyy

They are right.. I have two more problems

92. dinamix

u still did understand or what ??o.O

93. Destinyyyy

I understand how to solve that last one.

94. Destinyyyy

Can you help me with two more?

95. Destinyyyy

Im going to post them in a new question and tag you.

96. dinamix

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