Solve `x^2-x-1 lt 0`

Explanation

To solve the inequality \( x^2 - x - 1 < 0 \), we will follow these steps:

### Step 1: Find the roots of the quadratic equation
We start by finding the roots of the quadratic equation \( x^2 - x - 1 = 0 \) using the quadratic formula:

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