Answer
$x=\left\{ \dfrac{3-\sqrt{17}}{2},\dfrac{3+\sqrt{17}}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
x^2-3x-2=0
,$ use the Quadratic Formula.
$\bf{\text{Solution Details:}}$
In the equation above, $a=
1
,$ $b=
-3
,$ and $c=
-2
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{array}{l}\require{cancel}
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}
.\end{array}
The solutions are $
x=\left\{ \dfrac{3-\sqrt{17}}{2},\dfrac{3+\sqrt{17}}{2} \right\}
.$