# How do you solve sqrt(5(x+3))=10 and find any extraneous solutions?

Jun 2, 2016

Distribute inside the radical, and then square both sides.

#### Explanation:

$\sqrt{5 \left(x + 3\right)} = 10$

${\left(\sqrt{5 x + 15}\right)}^{2} = {10}^{2}$

$5 x + 15 = 100$

$5 x = 85$

$x = 17$

Since this is a radical equation, we must always check our answer back in the original equation to verify that there are no extraneous solutions. Checking, we find that $x = 17$ satisfies our equation; the solution set is $\left\{x = 17\right\}$.

Hopefully this helps!