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Math Help - Finding x

  1. #1
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    Finding x

    Hi,

    What rearrangements do you make to find x?:

    1/x = x - 2

    Apparently the answer is x = 1 + 2^0.5

    Please help!
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  2. #2
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    Quote Originally Posted by CSG18 View Post
    Hi,

    What rearrangements do you make to find x?:

    1/x = x - 2

    Apparently the answer is x = 1 + 2^0.5

    Please help!
    \frac{1}{x} = x - 2

    1 = x^2 - 2x

    0 = x^2 - 2x - 1

    0 = x^2 - 2x + (-1)^2 - (-1)^2 - 1

    0 = (x - 1)^2 - 2

    2 = (x - 1)^2

    \pm \sqrt{2} = x - 1

    1 \pm \sqrt{2} = x.
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  3. #3
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    Thank you very much. So you had to use completing the square. I understand now, but how would you know to use it?
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