Answer
$\left \{3 \pm 2\sqrt{ 5} \right \}$.
Work Step by Step
Apply the square root property to the given equation.
$\Rightarrow (x-3)^2=2^2\cdot 5$
$\Rightarrow (x-3)=\sqrt{(2^2\cdot 5)}$ or $(x-3)=-\sqrt{(2^2\cdot 5)}$
Simplify.
$\Rightarrow (x-3)=\sqrt{(2^2\cdot 5)}$ or $(x-3)=-\sqrt{(2^2\cdot 5)}$
$\Rightarrow x-3=2\sqrt{5}$ or $x-3=-2\sqrt{ 5}$
Add $3$ to both sides.
$\Rightarrow x-3+3=2\sqrt{5}+3$ or $x-3+3=-2\sqrt{ 5}+3$
Simplify.
$\Rightarrow x=3+2\sqrt{5}$ or $x=3-2\sqrt{ 5}$
The solution set is $\left \{ 3-2\sqrt{ 5},3+2\sqrt{5} \right \}$.
Or we can write.
$=\left \{3 \pm 2\sqrt{ 5} \right \}$.
