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Math Help - algebra problem I'm stuck on

  1. #1
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    algebra problem I'm stuck on

    \sqrt{\sqrt{x+5}+x}=5

    \sqrt{x+5} + x = 25

     (\sqrt{x+5})^2 = (25-x)^2

    x+5 = 625 - 50x - x^2

    0 = \frac{-x^2 = 49x + 620}{-1}

    0 = x^2 + 49x - 620

    Plug that into the quadratic equation and I get:

    x = \frac{-49 \pm \sqrt{4881}}{2}

    Which I can't find a way to simplify down.

    The book shows the answer to be 21. How they got it, I have no idea. So any help will be greatly appreciated
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mathgeek777 View Post
    \sqrt{\sqrt{x+5}+x}=5

    \sqrt{x+5} + x = 25

     (\sqrt{x+5})^2 = (25-x)^2

    x+5 = 625 - 50x {\color{red}+} x^2

    ...
    From here, you should get x^2-51x+620=0

    When solved you should get x=31 or x=20. I'll let you test these values. Only one is correct.

    The book answer is incorrect. 21 is not a possible solution for x.

    --Chris
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  3. #3
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    Its amazing how i seem to miss the tiniest details....

    Thanks for the help
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