Identify the relationship between x and a quadratic equation.

Step 1: Identify the relationship between $x$ and a quadratic equation.
The given value for $x$ is $x = \frac{1}{2}(1 - \sqrt{5})$.
Consider the quadratic equation $t^2 - t - 1 = 0$. Using the quadratic formula, its roots are:

$$t = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-1)}}{2(1)} = \frac{1 \pm \sqrt{1+4}}{2} = \frac{1 \pm \sqrt{5}}{2}$$

One of these roots is $t = \frac{1 - \sqrt{5}}{2}$, which is exactly our $x$.
Therefore, $x