The problem asks us to solve the quadratic equation $x^2 + x - 1 = 0$ using the quadratic formula.

1. Problem Description

The problem asks us to solve the quadratic equation $x^2 + x - 1 = 0$ using the quadratic formula.

2. Solution Steps

The quadratic formula is used to solve equations of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. The formula is given by:

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

In this case, $a=1$, $b=1$, and $c=-1$. Plugging these values into the quadratic formula, we get:

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

$x = \frac{-1 \pm \sqrt{1 + 4}}{2}$

$x = \frac{-1 \pm \sqrt{5}}{2}$

Thus, the two solutions are $x = \frac{-1 + \sqrt{5}}{2}$ and $x = \frac{-1 - \sqrt{5}}{2}$.

3. Final Answer

$\frac{-1 + \sqrt{5}}{2}, \frac{-1 - \sqrt{5}}{2}$