# Math Help - Solve Using the Square Root Method

1. ## Solve Using the Square Root Method

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

I thought this could only be used if k (the constant) was positive.

2. $\displaystyle \sqrt{(2x-1)^2}=\sqrt{-4}\Rightarrow 2x-1=\pm 2\mathbf{i}\Rightarrow x=\frac{1\pm 2\mathbf{i}}{2}$

3. You are right, this does not have any real solutions.

It does have two complex solutions though...

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

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

$\displaystyle 2x - 1 = \pm 2i$

$\displaystyle 2x = 1 \pm 2i$

$\displaystyle x = \frac{1}{2} \pm i$.

4. Yes, that's what I came up with, just wasn't certain it was correct.