# How do you solve x + 2 = sqrt(7 x) + 2?

Apr 26, 2018

$x = 0$ and $x = 7$

#### Explanation:

$x + 2 = \sqrt{7 x} + 2$

Subtract 2 on both sides

$\implies x = \sqrt{7 x}$

Square Both Sides

${x}^{2} = 7 x$

divide by $x$ on both sides (assuming $x \ne 0$)

$\implies x = 7$

However, we must check if $x = 0$ is a solution

$0 + 2 = \sqrt{7 \cdot 0} + 2$

$\implies 2 = 0 + 2$

This is true, so $x = 0$ is a solution!

Thus, $x = 0$ and $x = 7$