Solving $x^2 - x - 1 > 0$ I am having problems understanding how to solve:
$ x^2 - x - 1 > 0 $.
Any help would be much appreciated.

Hint
Completing the square, we obtain
$$
x^2-x-1
= \left(x-\frac{1}{2}\right)^2 - \frac{1}{4} - 1
= \left(x-\frac{1}{2}\right)^2 - \frac{5}{4}
=0.
$$
Then, rearrange terms and apply the square root to both side to get
$$
x - \frac{1}{2}
=\pm \frac{\sqrt{5}}{2}
\implies x=\frac {1\pm \sqrt{5}}{2}.
$$
Since the coefficient of $x^2$ is positive, then the expression is positive outside the roots.
