# How do you solve: sqrt(2x+5) - sqrt(x-2) = 3?

Apr 25, 2015

$\sqrt{2 x + 5} - \sqrt{x - 2} = 3$

1. First isolate one of the square roots:
$\sqrt{2 x + 5} = 3 + \sqrt{x - 2}$

2. Then square each side:
${\left(\sqrt{2 x + 5}\right)}^{2} = \left(3 + \sqrt{x - 2}\right) \left(3 + \sqrt{x - 2}\right)$
$2 x + 5 = 9 + 6 \sqrt{x - 2} + \left(x - 2\right)$

3. Simplify the equations leaving the square root on one sided:
$x - 2 = 6 \sqrt{x - 2}$

4. Square each side:
$\left(x - 2\right) \left(x - 2\right) = 36 \left(x - 2\right)$

5. Divide each side by (x-2):
$x - 2 = 36$
so $x = 38$

All ways check you answer in the original problem:
$\sqrt{2 x + 5} - \sqrt{x - 2} = 3$
$\sqrt{2 \left(38\right) + 5} - \sqrt{38 - 2} = 3$
$\sqrt{81} - \sqrt{36} = 3$
$9 - 6 = 3$
$3 = 3$