Answer
$x = 168$
Work Step by Step
First, isolate the radical on one side of the equation by adding $5$ to both sides of the equation:
$\sqrt{x+1}-5+5=8+5\\
\sqrt {x + 1} = 13$
Square both sides of the equation to get rid of the radical:
$(\sqrt{x+1})^2=13^2\\
x + 1 = 169\\
x=169-1\\
x = 168$
To check for extraneous solutions, substitute $168$ for $x$ into the original equation:
$\sqrt {168 + 1} - 5 = 8$
$\sqrt {169} - 5 = 8$
$13 - 5 = 8$
$8 = 8$
Both sides of the equation equal one another; therefore, the answer is correct. There are no extraneous solutions.
