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

Sep 28, 2015

See the explanation.

#### Explanation:

If $\sqrt{x + 6} = 3 + \sqrt{x}$, then

${\left(\sqrt{x + 6}\right)}^{2} = {\left(3 + \sqrt{x}\right)}^{2}$ (but not necessarily vie-versa)

So, $x + 6 = 9 + 6 \sqrt{x} + x$

Which would require
$- 3 = 6 \sqrt{x}$

But this is not possible, because $\sqrt{x}$ is never negative.

So, the equation has no solutions..