# How do you solve (2x)^(1/2)=x-4?

Feb 22, 2017

$\left\{8\right\}$

#### Explanation:

You're going to want to get rid of the 1/2 exponent. You can do this by squaring both sides.

${\left({\left(2 x\right)}^{\frac{1}{2}}\right)}^{2} = {\left(x - 4\right)}^{2}$

$2 x = \left(x - 4\right) \left(x - 4\right)$

$2 x = {x}^{2} - 4 x - 4 x + 16$

$0 = {x}^{2} - 10 x + 16$

$0 = \left(x - 8\right) \left(x - 2\right)$

$x = 8 \mathmr{and} 2$

This is a rational equation, so extraneous solutions are always a possibility, if not a likelihood. Always check your solutions.

(2 * 2)^(1/2) =^? 2 - 4

$\sqrt{2} \ne - 2 \textcolor{red}{\times}$

(2 * 8)^(1/2) =^? 8 - 4

$\sqrt{16} = 4$

The only valid solution is $x = 8$.

Hopefully this helps!