# How do you solve sqrt(x+6)-2=sqrt(x-2)?

Apr 29, 2016

$x = 3$

#### Explanation:

The question level implies no need for full explanation

Square both sides

${\left(\sqrt{x + 6} - 2\right)}^{2} = x - 2$

$\left(\cancel{x} + 6\right) - 4 \sqrt{x + 6} + 4 = \cancel{x} - 2$

$10 - 4 \sqrt{x + 6} = - 2$

$4 \sqrt{x + 6} = 12$

$\sqrt{x + 6} = 3$

square both sides

$x + 6 = 9$

$x = 3$