Answer
No solution.
Work Step by Step
The given equation is
$\Rightarrow r=\sqrt{-6r-5}$
Square both sides.
$\Rightarrow r^2=(\sqrt{-6r-5})^2$
Simplify.
$\Rightarrow r^2=-6r-5$
Move all terms to the left hand side.
$\Rightarrow r^2+6r+5=0$
Rewrite the middle term $6r$ as $5r+r$.
$\Rightarrow r^2+5r+r+5=0$
Factor out common terms.
$\Rightarrow r(r+5)+1(r+5)=0$
Factor out $(r+5)$.
$\Rightarrow (r+5)(r+1)=0$
Use zero product property.
$\Rightarrow r+5=0$ or $ r+1=0$
Solve for $r$.
$\Rightarrow r=-5$ or $ r=-1$.
Check $r=-5$.
$\Rightarrow -5=\sqrt{-6(-5)-5}$
$\Rightarrow -5=\sqrt{30-5}$
$\Rightarrow -5=\sqrt{25}$
$\Rightarrow -5=5$ Not true.
Check $r=-1$.
$\Rightarrow -1=\sqrt{-6(-1)-5}$
$\Rightarrow -1=\sqrt{6-5}$
$\Rightarrow -1=\sqrt{1}$
$\Rightarrow -1=1$ Not true.
Both the solutions are extraneous solutions.
Hence, the equation has no solution.
