Factorize the following expression : \(x^2 – 3x – 6\)

\[ x^2 – 3x – 6 \] \[ = x^2 – \frac{3 + \sqrt{33}}{2}x + \frac{-3 + \sqrt{33}}{2}x – 6 \] \[ = x\left(x – \frac{3 + \sqrt{33}}{2}\right) + \frac{-3 + \sqrt{33}}{2} \left(x – \frac{3 + \sqrt{33}}{2}\right) \] \[ = \left(x – \frac{3 + \sqrt{33}}{2}\right) \left(x + \frac{-3 + \sqrt{33}}{2}\right) \] \[ = \left(x – \frac{3 + \sqrt{33}}{2}\right) \left(x – \frac{3 – \sqrt{33}}{2}\right) \]