## iwanttogotostanford one year ago Find the solution of 3 times the square root of the quantity of x plus 6 equals negative 12, and determine if it is an extraneous solution.

1. iwanttogotostanford

@ospreytriple @BloomLocke367 @freckles

2. BloomLocke367

First off, can you write that in an equation?

3. iwanttogotostanford

yes

4. BloomLocke367

Do that first. Tell us what you get.

5. anonymous

You have$3\sqrt{x+6} = -12$What do you think we should do first?

6. iwanttogotostanford

$3\sqrt{x+6}=-12$

7. iwanttogotostanford

not sure

8. BloomLocke367

There are a few ways to do this, but the easiest would be to isolate the radical. Do you know how you would do that?

9. anonymous

Well we have to get the 'x' stuff all by itself, so how would you get rid of that 3?

10. iwanttogotostanford

square it?

11. BloomLocke367

you have to get rid of the 3 first. Right now, the 3 is being multiplied with $$\sqrt{x+6}$$. How do you "get rid of" something that is being multiplied?

12. iwanttogotostanford

divide

13. BloomLocke367

Yes! now divide both sides by 3 and tell me what you're left with

14. iwanttogotostanford

i don't have a calulator with me right now

15. BloomLocke367

You don't know $$-12\div 3$$?

16. iwanttogotostanford

yes its -4

17. BloomLocke367

There you go. so right now, you have $$\sqrt{x+6}=-4$$ correct?

18. iwanttogotostanford

yes

19. BloomLocke367

Now, how would you get rid of that radical?

20. iwanttogotostanford

hmm im not sure

21. BloomLocke367

Well, what's the opposite of taking the square root of something?

22. iwanttogotostanford

squaring it?

23. iwanttogotostanford

im clueless on this sorry

24. BloomLocke367

yes! so you have to square both sides :D

25. BloomLocke367

Don't apologize. You're doing great :D

26. iwanttogotostanford

okay, thanks!

27. iwanttogotostanford

so it would be x^2+36=16?

28. BloomLocke367

No, because when you squared it, it just cancelled out the radical. For instance, when you take $$\sqrt1^2$$, you don't get $$1^2$$ do you? No, you just get 1. Try again. The right side is correct.

29. iwanttogotostanford

so, x+6=16?

30. BloomLocke367

Yep!

31. iwanttogotostanford

ok, thanks! so then it would be x=10 right?

32. iwanttogotostanford

and would it be extraneous or not extraneous though?

33. BloomLocke367

mhm, I'm pretty certain. Let me ask @Nnesha if I did this correctly. Now we just have to check to make sure it's not extraneous. Do you know what an extraneous solution is?

34. Nnesha

did a great job!

35. BloomLocke367

Okay, thanks. lol @iwanttogotostanford do you know what an extraneous solution is?

36. iwanttogotostanford

@BloomLocke367 yes

37. BloomLocke367

Then graph it and find out if there's a point where x=4

38. iwanttogotostanford

do you know if it is or not? I'm sorry I'm just in a very hard place right now to be graphing things (I'm on a plane)

39. Nnesha

you can substitute x for 10 into the original equation to find out if it's extraneous or not. :=)

40. iwanttogotostanford

thanks! @Nnesha

41. BloomLocke367

Sorry, I was afk. Thanks @Nnesha

42. Nnesha

np

43. Nnesha

if you get equal sides then it's not extraneous if both sides are not equal then 10 would be an extraneous

44. iwanttogotostanford

ok thanks do u know if it is or not? @Nnesha

45. BloomLocke367

oops, I don't know why I said 4 earlier, I meant to say 10. lol

46. Nnesha

no i don't. you have to figure it out!

47. iwanttogotostanford

@Nnesha well i don't have paper with me so its really hard

48. Nnesha

welll, you can use paint

49. Nnesha

that would be fun! trust me

50. iwanttogotostanford

ok, thank you @Nnesha

51. iwanttogotostanford

i got extraneous:-)

52. Nnesha

both sides are equal ?

53. iwanttogotostanford

no they aren't equal

54. BloomLocke367

There you go!

55. iwanttogotostanford

thanks!

56. Nnesha

o^_^o

57. iwanttogotostanford

they aren't equal= not extraneous?

58. BloomLocke367

You were correct the first time, it is extraneous because they are not equal.

59. BloomLocke367

wait....

60. Nnesha

both sides are not equal = extraneous both sides are equal = non-extraneous

61. BloomLocke367

when you take the square root of something, it could be positive or negative

62. BloomLocke367

Right @Nnesha?

63. Nnesha

something if you mean square root of negative number then you will get imaginary solution if you take square root of positive then you would always get positive answer

64. iwanttogotostanford

i think its non-extraneous

65. BloomLocke367

how so? because -4*-4=16 AND 4*4=16

66. iwanttogotostanford

oh whoops i did -4 times 4

67. Nnesha

$\huge\rm 3\sqrt{10+16}=-12$ whet did you get at left side ?

68. iwanttogotostanford

i get it now

69. BloomLocke367

I gotta go, sorry!

70. Nnesha

i said number if -4 times -4 = positive number so square root would be positive

71. Nnesha

so it's extraneous or non-extraneous ?

72. iwanttogotostanford

ok it is extraeous then

73. Nnesha

yes right $12\cancel{=}-12$

74. iwanttogotostanford

thank you @Nnesha

75. Nnesha

np