# How do you solve sqrt( x^2+7)=x+1?

May 8, 2016

$x = 3$

#### Explanation:

First square both sides, noting that squaring may introduce spurious solutions...

${x}^{2} + 7 = {\left(x + 1\right)}^{2} = {x}^{2} + 2 x + 1$

Subtract ${x}^{2}$ from both ends to get:

$7 = 2 x + 1$

Subtract $1$ from both sides to get:

$6 = 2 x$

Divide both sides by $2$ and transpose to get:

$x = 3$

Check that this is a solution of the original equation:

$\sqrt{{x}^{2} + 7} = \sqrt{{3}^{2} + 7} = \sqrt{9 + 7} = \sqrt{16} = 4 = 3 + 1 = x + 1$