Answer
$1,-2$
Work Step by Step
The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$
where $det =\begin{bmatrix}p & q \\
r & s\end{bmatrix}$
After simplifying, this matrix yields: $4=(x)(x+1) - (2)(-1) $
or, $x^2+x-2=0$
or, $(x^2+x+\dfrac{1}{4})-2=0+\dfrac{1}{4}$
or, $(x+\dfrac{1}{4})^2=\dfrac{9}{4} \implies x=-\dfrac{1}{2} \pm \sqrt{\dfrac{9}{4}}$
So, $x=1,-2$
