# How do you solve  sqrt(6x+1) = 3sqrt(x)-1?

May 24, 2016

$x = 0$ or $x = 4$

#### Explanation:

Squaring both sides of $\sqrt{6 x + 1} = 3 \sqrt{x} - 1$, we get

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

or $6 \sqrt{x} = 9 x + 1 - 6 x - 1$

or $6 \sqrt{x} = 3 x$

or $2 \sqrt{x} = x$ - now squaring this

$4 x = {x}^{2}$ or ${x}^{2} - 4 x = 0$

or $x \left(x - 4\right) = 0$

Hence $x = 0$ or $x = 4$