Answer
$\{-2\pm5i\}$.
Work Step by Step
Subtract $25$ from both sides of the given equation.
$\Rightarrow (x+2)^2+25-25=0-25$
Simplify.
$\Rightarrow (x+2)^2=-25$
Apply the Square Root Property.
$\Rightarrow x+2=+\sqrt{-25}$ or $x+2=-\sqrt{-25}$
Sinplify.
$\Rightarrow x+2=+\sqrt{5^2}\sqrt{-1}$ or $x+2=-\sqrt{5^2}\sqrt{-1}$
Use $\sqrt{-1}=i$
$\Rightarrow x+2=+5i$ or $x+2=-5i$
Subtract $2$ from both sides.
$\Rightarrow x+2-2=+5i-2$ or $x+2-2=-5i-2$
Simplify.
$\Rightarrow x=-2+5i$ or $x=-2-5i$
Or we can write.
$\Rightarrow x=-2\pm5i$.
The solution set is $\{-2\pm5i\}$.
