# How do you solve sqrt(x+5)=1-x ?

May 14, 2016

$\sqrt{x + 5} = 1 - x$

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

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

$0 = {x}^{2} - 3 x - 4$

$0 = \left(x - 4\right) \left(x + 1\right)$

$x = 4 \mathmr{and} - 1$

However, after checking in the original equation we find that only $x = - 1$ works.

The solution set is $\left\{- 1\right\}$.

Hopefully this helps!