# How do you solve sqrt(x^2+5)=x+3?

Jul 14, 2016

Square both sides of the equation.

#### Explanation:

${\left(\sqrt{{x}^{2} + 5}\right)}^{2} = {\left(x + 3\right)}^{2}$

${x}^{2} + 5 = {x}^{2} + 6 x + 9$

${x}^{2} - {x}^{2} - 6 x + 5 - 9 = 0$

$- 6 x = 4$

$x = - \frac{2}{3}$

Checking in the original equation, we find this solution works. Hence, the solution set is $\left\{- \frac{2}{3}\right\}$.

Hopefully this helps!