Answer
$\{-3,3,-2,2\}$.
Work Step by Step
Substitute $x^2 = A$ in the given equation.
$\Rightarrow A^2-13A+36=0$
Rewrite the middle term $-13A$ as $-9A-4A$.
$\Rightarrow A^2-9A-4A+36=0$
Group terms.
$\Rightarrow (A^2-9A)+(-4A+36)=0$
Factor each term.
$\Rightarrow A(A-9)-4(A-9)=0$
Factor out $(A-9)$.
$\Rightarrow (A-9)(A-4)=0$
Set each factor equal to zero.
$\Rightarrow A-9=0$ or $A-4=0$
Isolate $A$.
$\Rightarrow A=9$ or $A=4$
Substitute back $A=x^2$.
$\Rightarrow x^2=9$ or $x^2=4$
Use the Square Root Property.
$\Rightarrow x=+\sqrt{9}$ or $x=-\sqrt{9}$ or $x =+\sqrt{4}$ or $x =-\sqrt{4}$
$\Rightarrow x=+\sqrt{3^2}$ or $x=-\sqrt{3^2}$ or $x =+\sqrt{2^2}$ or $x =-\sqrt{2^2}$
Simplify.
$\Rightarrow x=3$ or $x=-3$ or $x =2$ or $x =-2$
The solution set is $\{-3,3,-2,2\}$.
