Answer
$x = 12$
Work Step by Step
First, isolate the radical by adding $3$ to both sides of the equation:
$\sqrt {4x - 23} = 5$
Square both sides of the equation to eliminate the radical:
$(\sqrt {4x - 23})^2 = 5^2$
$4x - 23 = 25$
Add $23$ to both sides of the equation to isolate the $x$ term:
$4x = 48$
Divide both sides of the equation by $4$ to solve for $x$:
$x = 12$
Check if the solution is valid by substituting $12$ to $x$ in the given equation:
$\begin{align*}
\sqrt{4x-23}-3&=2\\
\sqrt{4(12)-23}-3&=2\\
\sqrt{25}-3&=2\\
5-3&=2\\
2&=2
\end{align*}$
Thus, the solution is $x=12$.
