# What is the value of x if sqrt(5x+1) = x+1?

Apr 30, 2015

$x \in \left\{0 , 3\right\}$

#### Explanation:

$\sqrt{5 x + 1} = x + 1$

$5 x + 1 = {\left(x + 1\right)}^{2}$

$5 x + 1 = {x}^{2} + 2 x + 1$

${x}^{2} - 3 x = 0$

$x \left(x - 3\right) = 0$

Either $x = 0$ or $\left(x - 3\right) = 0$

The solutions are
$x = 0$ and $x = 3$