A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

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.

  • This Question is Closed
  1. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ospreytriple @BloomLocke367 @freckles

  2. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    First off, can you write that in an equation?

  3. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  4. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Do that first. Tell us what you get.

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  6. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[3\sqrt{x+6}=-12\]

  7. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    not sure

  8. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  10. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    square it?

  11. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    divide

  13. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  14. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i don't have a calulator with me right now

  15. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You don't know \(-12\div 3\)?

  16. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes its -4

  17. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  18. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  19. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Now, how would you get rid of that radical?

  20. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm im not sure

  21. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  22. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    squaring it?

  23. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    im clueless on this sorry

  24. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes! so you have to square both sides :D

  25. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  26. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay, thanks!

  27. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  28. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so, x+6=16?

  30. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yep!

  31. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  32. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and would it be extraneous or not extraneous though?

  33. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    did a great job!

  35. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  36. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @BloomLocke367 yes

  37. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  38. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  40. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks! @Nnesha

  41. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Sorry, I was afk. Thanks @Nnesha

  42. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    np

  43. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  44. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  45. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  46. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  47. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  48. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    welll, you can use `paint`

  49. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that would be fun! trust me

  50. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, thank you @Nnesha

  51. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i got extraneous:-)

  52. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    both sides are equal ?

  53. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no they aren't equal

  54. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    There you go!

  55. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks!

  56. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    o^_^o

  57. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    they aren't equal= not extraneous?

  58. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  59. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    wait....

  60. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  61. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  62. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Right @Nnesha?

  63. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    `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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i think its non-extraneous

  65. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

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

  66. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh whoops i did -4 times 4

  67. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  68. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i get it now

  69. BloomLocke367
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I gotta go, sorry!

  70. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  71. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so it's extraneous or non-extraneous ?

  72. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok it is extraeous then

  73. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes right \[12\cancel{=}-12\]

  74. iwanttogotostanford
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thank you @Nnesha

  75. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    np

  76. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.