# sqrt( x^2 + 5) = x + 1? solve the equation

Apr 13, 2017

$x = 2$

#### Explanation:

$\sqrt{{x}^{2} + 5} = x + 1$

${x}^{2} + 5 = {\left(x + 1\right)}^{2} = {x}^{2} + 2 x + 1$

${x}^{2} + 5 = {x}^{2} + 2 x + 1$

$2 x - 4 = 0$

$x = 2$

Verify solution using original equation

$\sqrt{{2}^{2} + 5} = 3$

$2 + 1 = 3$

$x = 2$ is a valid solution