# How do you solve 4 sqrt (x) = 8 + 2 sqrt (x)?

Sep 13, 2015

color(green)(x = 16

#### Explanation:

We are given that $4 \sqrt{x} = 8 + 2 \sqrt{x}$

Transposing $2 \sqrt{x}$ to the left hand side, we get:

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

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

$2 \sqrt{x} = 8$

Divising both sides by 2, we get:

$\frac{\cancel{2} \sqrt{x}}{\cancel{2}} = \frac{8}{2}$

$\sqrt{x} = 4$

Squaring both sides we get:

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

In exponents, color(blue)(sqrta*sqrta = a

Hence we get color(green)(x = 16