Answer
$r=7$
Work Step by Step
The given equation is
$\Rightarrow -1=\sqrt {5r+1}-7$
Add $7$ to each side.
$\Rightarrow -1+7=\sqrt {5r+1}-7+7$
Simplify.
$\Rightarrow 6=\sqrt {5r+1}$
Square each side of the equation.
$\Rightarrow 6^2=(\sqrt{5r+1})^2$
Simplify.
$\Rightarrow 36=5r+1$
Subtract $1$ from each side.
$\Rightarrow 36-1=5r+1-1$
Simplify.
$\Rightarrow 35=5r$
Divide each side by $5$.
$\Rightarrow \frac{35}{5}=\frac{5r}{5}$
Simplify.
$\Rightarrow 7=r$
Check $r=7$.
$\Rightarrow -1=\sqrt {5r+1}-7$
$\Rightarrow -1=\sqrt {5(7)+1}-7$
$\Rightarrow -1=\sqrt {35+1}-7$
$\Rightarrow -1=\sqrt {36}-7$
$\Rightarrow -1=\sqrt {6^2}-7$
$\Rightarrow -1=6-7$
$\Rightarrow -1=-1$
True.
Hence, the solution is $r=7$.
