Answer
$x=12$
Work Step by Step
The given equation is
$\Rightarrow \sqrt{x+4}+7=11$
Subtract $7$ from each side.
$\Rightarrow \sqrt{x+4}+7-7=11-7$
Simplify.
$\Rightarrow \sqrt{x+4}=4$
Square each side of the equation.
$\Rightarrow (\sqrt{x+4})^2=4^2$
Simplify.
$\Rightarrow x+4=16$
Subtract $4$ from each side.
$\Rightarrow x+4-4=16-4$
Simplify.
$\Rightarrow x=12$
Check $x=12$.
$\Rightarrow \sqrt{x+4}+7=11$
$\Rightarrow \sqrt{12+4}+7=11$
$\Rightarrow \sqrt{16}+7=11$
$\Rightarrow 4+7=11$
$\Rightarrow 11=11$
True.
Hence, the solution is $x=12$.
