Answer
$x = -0.32~~$ or $~~x = 6.32$
Work Step by Step
A quadratic equation can be written in this form:
$ax^2 + bx+c = 0$
where $a,b,$ and $c$ are real numbers and $a \neq 0$
We can determine the values of $a, b,$ and $c$:
$x^2-6x -2 = 0$
$a = 1$
$b = -6$
$c = -2$
We can use the quadratic formula to find the solutions of the equation:
$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
$x = \frac{-(-6) \pm \sqrt{(-6)^2-(4)(1)(-2)}}{(2)(1)}$
$x = \frac{6 \pm \sqrt{36+8}}{2}$
$x = \frac{6 \pm \sqrt{44}}{2}$
$x = \frac{6 - \sqrt{44}}{2}~~$ or $~~x = \frac{6 + \sqrt{44}}{2}$
$x = -0.32~~$ or $~~x = 6.32$
