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Math Help - radicals HELP!!!!! URGENT!!!!!

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    Question radicals HELP!!!!! URGENT!!!!!

    sq. rt. (x-7) + sq. rt. (x) =4
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    Quote Originally Posted by iheartthemusic29 View Post
    sq. rt. (x-7) + sq. rt. (x) =4
    \sqrt{x - 7} + \sqrt{x} = 4

    The trick here is to divide and conquer. You want to isolate one of the square roots on one side of the equation. So:
    \sqrt{x - 7} = 4 - \sqrt{x} <-- Square both sides

    x - 7 = \left ( 4 - \sqrt{x} \right ) ^2

    x - 7 = 16 - 8\sqrt{x} + x

    Now do it again:
    \sqrt{x} =\frac{23}{8}

    x = \left ( \frac{23}{8} \right ) ^2 = \frac{529}{64}

    Always always always check your solutions in the original equation:
    \sqrt{\frac{529}{64} - 7} + \sqrt{\frac{529}{64}} = 4

    \sqrt{\frac{81}{64}} + \frac{23}{8} = 4

    \frac{9}{8} + \frac{23}{8} = 4

    \frac{32}{8} = 4

    4 = 4 (Check!)

    -Dan
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