Đáp án:
$\begin{array}{l}
{x^2} - x - 3\\
= {x^2} - 2.x.\frac{1}{2} + \frac{1}{4} - \frac{{13}}{4}\\
= {\left( {x - \frac{1}{2}} \right)^2} - \frac{{13}}{4}\\
= {\left( {x - \frac{1}{2}} \right)^2} - {\left( {\frac{{\sqrt {13} }}{2}} \right)^2}\\
= \left( {x - \frac{1}{2} - \frac{{\sqrt {13} }}{2}} \right)\left( {x - \frac{1}{2} + \frac{{\sqrt {13} }}{2}} \right)\\
= \left( {x - \frac{{1 + \sqrt {13} }}{2}} \right)\left( {x + \frac{{ - 1 + \sqrt {13} }}{2}} \right)
\end{array}$
