Answer
$x = 5$
Work Step by Step
Square both sides of the equation to eliminate the exponent:
$\left((2x)^{1/2}\right)^2=\left(x+5)^{1/2}\right)^2\\
2x = x + 5\\
2x-x=5\\
x=5$
To check if we have an extraneous solution, we substitute the solution into the original equation to see if the two sides equal one another.
$\sqrt {2(5)} = \sqrt {5 + 5}$
Simplify the radicands:
$\sqrt {10} = \sqrt {10}$
Both sides are equal; therefore, this solution is valid.
