# How do you solve sqrt(6x - 8) = x ?

Oct 2, 2017

$x = 2 \text{ }$ or $\text{ } x = 4$

#### Explanation:

Given:

$\sqrt{6 x - 8} = x$

Note that $\sqrt{\ldots} \ge 0$. So we require $x \ge 0$

Square both sides of the given equation (noting that this may introduce extraneous solutions), to get:

$6 x - 8 = {x}^{2}$

Subtract $6 x - 8$ from both sides to get:

$0 = {x}^{2} - 6 x + 8 = \left(x - 4\right) \left(x - 2\right)$

So:

$x = 2 \text{ }$ or $\text{ } x = 4$

Since these are both positive, they are both solutions of the original equation.