## Algebra and Trigonometry 10th Edition

$-2,3$
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: $0=(x+4)(x-5) - (-2)(7)$ We need to set the expression equal to $0$. Thus, we have: $x^2-x-6=0$ or, $(x-3)(x+2)=0$ So, $x=-2,3$