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Math

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The following are the last two problems on my test review. I am trying to study for a test. This is not my homework. I am not expecting anyone to do my homework for me. I just need to get the answers to be able to study and if you can help, I would really really appreciate it!

1. solve the equation. (9n+1)squared=0
2. solve the equation by completing the square. xsquared+x+7=0

  • Math -

    (9n+1)^2 = 0
    9n+1 = 0
    9n = -1
    n = -1/9

    x^2 + x = -7
    x^2 + x + 1/4 = -7 + 1/4
    (x+1/2)^ = -27/4
    x+1 = ± √-27 /2
    x = -1 ±3i√3/2
    = (-2 ± 3i√3)/2

  • Math -

    Hi, thank you for your time Reiny and your info. I am so sorry but on the first one I accidentally put 0 where I should have put =9. In other words, the first equation should have said (9n+1)squared =9. Really sorry to have taken up your time with the wrong equation, but if you are able to help me out again, with the right one, I would appreciate it. Also, I am unfamiliar with the sign you use that looks like a check mark, could you please advise what the sign means? Thanks for your help!

  • Math -

    (9n+1)squared = 9
    We expand the term with the square:
    (81n^2 + 18n + 1) = 9
    81n^2 + 18n + 1 - 9 = 0
    81n^2 + 18n - 8 = 0
    Factoring,
    (9n + 4)(9n - 2) = 0
    n = -4/9 and n = 2/9
    Note that there are two values of n.

    The sign that looks like a check mark in #2 is a squareroot sign.

    I'm not Reiny but I hope you can trust my answer.
    Hope this helps :3

  • Math -

    The answer is good, but it might have been a lot simpler to solve it the way Reiny did:

    (9n+1)^2 = 9
    9n+1 = ±3
    9n = ±3-1
    9n = -4,2
    n = -4/9,2/9

  • Math -

    (81n^3+18n^2-62n+3)/(9n+1)

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