# How do you simplify sqrt(5x-4)-sqrt(x+8)=2?

Sep 2, 2016

The solution set is $\left\{8\right\}$.

#### Explanation:

Isolate one of the sqrt's.

$\sqrt{5 x - 4} = 2 + \sqrt{x + 8}$

Square both sides of the equation:

${\left(\sqrt{5 x - 4}\right)}^{2} = {\left(2 + \sqrt{x + 8}\right)}^{2}$

$5 x - 4 = 4 + 4 \sqrt{x + 8} + x + 8$

$4 x - 16 = 4 \sqrt{x + 8}$

$4 \left(x - 4\right) = 4 \sqrt{x + 8}$

$x - 4 = \sqrt{x + 8}$

Square again:

${\left(x - 4\right)}^{2} = {\left(\sqrt{x + 8}\right)}^{2}$

${x}^{2} - 8 x + 16 = x + 8$

${x}^{2} - 9 x + 8 = 0$

$\left(x - 8\right) \left(x - 1\right) = 0$

$x = 8 \mathmr{and} 1$

Checking in the original equation, you will find that $x = 8$ works while $x = 1$ is extraneous.

Hopefully this helps!