# How do you solve sqrt(x+2)-x=0?

##### 1 Answer
Jun 17, 2018

$x = 2$

#### Explanation:

Rearrange to get the square root on one side on its own:
$\sqrt{x + 2} - x = 0$
$\sqrt{x + 2} = x$

Square it out to get a quadratic:
$x + 2 = {x}^{2}$
${x}^{2} - x - 2 = 0$

Quadratic formula:
$x = \frac{1}{2} \left(1 \pm \sqrt{1 + 8}\right)$
$x = \frac{1}{2} \left(1 \pm 3\right)$
$x = - 1 , 2$

But when we square in our working we need to check that we haven't accidentally introduced extra roots. In this case we have: -1 is not a solution of the original equation, although 2 is.

So there is one solution: $x = 2$.