The problem is to solve the quadratic equation $x^2 + x - 8 = 0$ using the quadratic formula.

1. Problem Description

The problem is to solve the quadratic equation $x^2 + x - 8 = 0$ using the quadratic formula.

2. Solution Steps

The quadratic formula is given by

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

for the quadratic equation $ax^2 + bx + c = 0$.

In our case, $a = 1$, $b = 1$, and $c = -8$.

Substituting these values into the quadratic formula, we get

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

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

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

3. Final Answer

The solutions are $\frac{-1 + \sqrt{33}}{2}, \frac{-1 - \sqrt{33}}{2}$.