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Math Help - Solve Using the Square Root Method

  1. #1
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    Solve Using the Square Root Method

    $(2x-1)^{2}=-4$

    I thought this could only be used if k (the constant) was positive.
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  2. #2
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    \displaystyle \sqrt{(2x-1)^2}=\sqrt{-4}\Rightarrow 2x-1=\pm 2\mathbf{i}\Rightarrow x=\frac{1\pm 2\mathbf{i}}{2}
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  3. #3
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    You are right, this does not have any real solutions.

    It does have two complex solutions though...

    \displaystyle (2x - 1)^2 = -4

    \displaystyle 2x - 1 = \pm \sqrt{-4}

    \displaystyle 2x - 1 = \pm 2i

    \displaystyle 2x = 1 \pm 2i

    \displaystyle x = \frac{1}{2} \pm i.
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  4. #4
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    Yes, that's what I came up with, just wasn't certain it was correct.
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