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Math Help - how to factor this

  1. #1
    Senior Member sakonpure6's Avatar
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    how to factor this

    0=2cos^2x + 2*sqrt2 * cos x + 1

    When I tried the quadratic formula, the discriminant was equal to zero. So i know this can be factored, but i do not know how to deal with sqrt2.

    Thank you for your time
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  2. #2
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    Re: how to factor this

    \displaystyle \begin{align*} 0 &= 2\cos^2{(x)} + 2\sqrt{2}\cos{(x)} + 1 \\ 0 &= \cos^2{(x)} + \sqrt{2}\cos{(x)} + \frac{1}{2} \\ 0 &= \cos^2{(x)} + \sqrt{2}\cos{(x)} + \left( \frac{\sqrt{2}}{2} \right) ^2 - \left( \frac{\sqrt{2}}{2} \right) ^2 + \frac{1}{2} \\ 0 &= \left[ \cos{(x)} + \frac{\sqrt{2}}{2} \right] ^2 - \frac{1}{2} + \frac{1}{2} \\ 0 &= \left[ \cos{(x)} + \frac{\sqrt{2}}{2} \right] ^2 \end{align*}
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  3. #3
    Senior Member sakonpure6's Avatar
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    Re: how to factor this

    Wow nice!!!, I have a question, how did you know to add and subtract the (sqrt2 / 2)^2 ?? Is it from experience?
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  4. #4
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    Re: how to factor this

    Completing the Square.
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