#### Answer

$$\pm1$$

#### Work Step by Step

For cross multiplication, we know:
$$\frac{a}{d} =\frac{b}{c} \rightarrow ac=bd$$
Thus, we find:
$$xx=-\left(x^2-2\right)\cdot \:1 \\ x^2=-\left(x^2-2\right)\\ x=\pm1$$
Checking our solution by plugging the given value back into the equation, we assure that the solutions are not extraneous.