Answer: \(x = 4 \text{ or } x = -5\)
Half of the coefficient of \(x\) is \(\frac{1}{2}\); add and subtract \(\frac{1}{4}\).
\[x^2 + x + \frac{1}{4} - \frac{1}{4} - 20 = 0\]\[\left(x + \frac{1}{2}\right)^2 = \frac{81}{4}\]\[x + \frac{1}{2} = \pm\frac{9}{2}\]\(x = -\frac{1}{2} + \frac{9}{2} = 4\) or \(x = -\frac{1}{2} - \frac{9}{2} = -5\).