Answer
$x=6$
Work Step by Step
Add $5$ to both sides:
$\sqrt{4x+1}-5+5=0+5$
$\sqrt{4x+1}=5$
Square both sides:
$(\sqrt{4x+1})^2=(5)^2$
$4x+1=25$
Subtract $1$ from both sides:
$4x+1-1=25-1$
$4x=24$
Divide both sides by $4$:
$\dfrac{4x}{4}=\dfrac{24}{4}$
$x=6$
Substitute into original problem to check for extraneous solutions:
$\sqrt{4(6)+1}-5=0$
$\sqrt{24+1}-5=0$
$\sqrt{25}-5=0$
$5-5=0$
$0=0$
