# How do you solve sqrt(x - 3) + sqrt(x + 5) = 4?

Jun 6, 2018

$\rightarrow \sqrt{x - 3} + \sqrt{x + 5} = 4$

$\rightarrow {\left(\sqrt{x - 3}\right)}^{2} = {\left(4 - \sqrt{x + 5}\right)}^{2}$

$\rightarrow \cancel{x} - 3 = 16 - 8 \sqrt{x + 5} \cancel{+ x} + 5$

$\rightarrow 8 \sqrt{x + 5} = 24$

$\rightarrow \sqrt{x + 5} = 3$

$\rightarrow x + 5 = 9$

$\rightarrow x = 4$