# How do you solve sqrt(u+6)=u and check your solution?

Jul 13, 2017

$u = 3$

#### Explanation:

$\sqrt{u + 6} = u$

$u + 6 = {u}^{2}$ $\to$square both sides to get rid of radical

$0 = {u}^{2} - u - 6$ $\to$subtract $6$ and $u$ to bring all terms to one side

$0 = \left(u - 3\right) \left(u + 2\right)$ $\to$ factor

There are two possibilities:

$0 = u - 3$
$\implies u = 3$

$0 = u + 2$
$\implies u = - 2$

To check your solutions, substitute them back into the original equation.

$u = 3$

$\sqrt{u + 6} = u$
$\sqrt{3 + 6} = 3$
$\sqrt{9} = 3$
$3 = 3$ $\to$works

$u = - 2$

$\sqrt{u + 6} = u$
$\sqrt{- 2 + 6} = - 2$
$\sqrt{4} = - 2$
$2 = - 2$ $\to$does not work

So, the only solution is $u = 3$.