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Math Help - Quick Simplify

  1. #1
    Raj
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    Quick Simplify

    Ok so im trying to find the roots of (x+2)(4x^2-8x-3)

    I went and used the Quadratic Formula to get

    x = \frac{8 \pm \sqrt{(-8)^2 - 4(4)(-3)}}{8}

    x = \frac{8 \pm \sqrt{112}}{8}

    Now this is where i get stuck
    I want to leave it as a radical*
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  2. #2
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    Simplifying…

    Use the fact that 112 = 16*7

    --Kevin C.
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  3. #3
    Raj
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    Quote Originally Posted by TwistedOne151 View Post
    Use the fact that 112 = 16*7

    --Kevin C.
    x = \frac{8 \pm 4\sqrt{7}}{8}

    It can be simplified more though,

    my text says x = \frac{2 \pm 2\sqrt{7}}{2} but how//
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  4. #4
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    Simplifying…

    Note that 8=4*2, so x = \frac{8 \pm 4\sqrt{7}}{8} = \frac{4 \cdot 2 \pm 4\sqrt{7}}{4 \cdot 2}= \frac{4 (2 \pm \sqrt{7})}{4 \cdot 2} and we cancel the 4s in the numerator and denominator to get x = \frac{2 \pm \sqrt{7}}{2}.

    --Kevin C.
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