Answer
$x_1=2$ and $x_2=-1$
Work Step by Step
$e^x=e^{x^2-2}$
Using the One-to-One Property:
$x^2-2=x$
$x^2-x-2=0~$ ($a=1,~b=-1,~c=-2$):
$x=\frac{-(-1)±\sqrt {(-1)^2-4(1)(-2)}}{2(1)}=\frac{1±\sqrt 9}{2}=\frac{1±3}{2}$
$x_1=\frac{4}{2}=2$ and $x_2=\frac{-2}{2}=-1$
