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Math Help - Solve for x

  1. #1
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    Solve for x

     <br />
\frac{(2x-14)+12(\sqrt{x+2})}{\sqrt{x+2}}=0<br />
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  2. #2
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    Quote Originally Posted by Punch View Post
     <br />
\frac{(2x-14)+12(\sqrt{x+2})}{\sqrt{x+2}}=0<br />
    From the domain x  > -2

    (2x-14) + 12\sqrt{x+2} = 0

    2(x-7) = -12 \sqrt{x+2}

    Cancel out 2 then square:

    x^2-14x+49 = 36x+72

    x^2-50x-23 = 0

    23 is prime and so solve using quadratic formula

    x = \frac{50 \pm \sqrt{50^2-4 \cdot 1 \cdot -23}}{2}

    x= 25 \pm 18 \sqrt{2}

    However, if we put these solutions back into the original equation we find that 25 + 18\sqrt{2} \neq 0 - it is an extraneous root so it should be discarded

    x= 25 - 18 \sqrt{2} does equal 0 when put into the original equation so this is a root
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  3. #3
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    The numerator must be zero, so ignore the denominator, except to see limitations of acceptable values [x NOT<=-2 or it is undefined or complex.]

    Divide by 2 to simplify.

    Move the radical to one side [watch for sign change] and square both sides.

    Give it a try.
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