Answer
$\color{blue}{\left\{\dfrac{3-\sqrt{17}}{2}, \dfrac{3+\sqrt{17}}{2}\right\}}$.
Work Step by Step
RECALL:
The quadratic equation $ax^2+bx+c=0$ can be solved using the quadratic formula:
$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$
The given equation has:
$a=1, b=-3, c=-2$
Substitute these values into the quadratic formula to obtain:
$x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-2)}}{2(1)}
\\x=\dfrac{3\pm\sqrt{9+8}}{2}
\\x=\dfrac{3\pm\sqrt{17}}{2}$
Thus, the solution set is $\color{blue}{\left\{\dfrac{3-\sqrt{17}}{2}, \dfrac{3+\sqrt{17}}{2}\right\}}$.
