The problem asks us to solve the quadratic equation $x^2 - x - 8 = 0$ using the quadratic formula. We need to express the answer in simplified form, using radicals if necessary.

1. Problem Description

The problem asks us to solve the quadratic equation $x^2 - x - 8 = 0$ using the quadratic formula. We need to express the answer in simplified form, using radicals if necessary.

2. Solution Steps

The quadratic formula is used to solve equations of the form $ax^2 + bx + c = 0$. The formula is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In our case, $a = 1$, $b = -1$, and $c = -8$. Plugging these values into the quadratic formula gives:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-8)}}{2(1)}$

$x = \frac{1 \pm \sqrt{1 + 32}}{2}$

$x = \frac{1 \pm \sqrt{33}}{2}$

Thus, the two solutions are $x = \frac{1 + \sqrt{33}}{2}$ and $x = \frac{1 - \sqrt{33}}{2}$.

3. Final Answer

$\frac{1 + \sqrt{33}}{2}, \frac{1 - \sqrt{33}}{2}$