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

Aug 19, 2016

$x = \frac{1}{2}$

#### Explanation:

Lets get rid of the square root on the left hand side (LHS)

Square both sides giving:

$2 x + 3 = {\left(3 - \sqrt{2 x}\right)}^{2}$

$\cancel{2 x} + 3 = 9 - 6 \sqrt{2 x} + \cancel{2 x}$

$\sqrt{2 x} = \frac{9 - 3}{6} = + 1$

square both sides again

$2 x = 1 \implies x = \frac{1}{2}$