Answer
The solution is $c=5$.
Work Step by Step
The given equation is
$\Rightarrow 19-4\sqrt{3c-11}=11$
Subtract $19$ from each side.
$\Rightarrow 19-4\sqrt{3c-11}-19=11-19$
Simplify.
$\Rightarrow -4\sqrt{3c-11}=-8$
Divide each side by $-4$.
$\Rightarrow \sqrt{3c-11}=2$
Square each side of the equation.
$\Rightarrow (\sqrt{3c-11})^2=(2)^2$
Simplify.
$\Rightarrow 3c-11=4$
Add $11$ to each side.
$\Rightarrow 3c-11+11=4+11$
Simplify.
$\Rightarrow 3c=15$
Divide each side by $3$.
$\Rightarrow c=5$
Check $c=5$.
$\Rightarrow 19-4\sqrt{3c-11}=11$
$\Rightarrow 19-4\sqrt{3(5)-11}=11$
$\Rightarrow 19-4\sqrt{15-11}=11$
$\Rightarrow 19-4\sqrt{4}=11$
$\Rightarrow 19-4(2)=11$
$\Rightarrow 19-8=11$
$\Rightarrow 11=11$
True.
Hence, the solution is $c=5$.
