# How do you complete the square for y=x^2 - 9x?

$y = {\left(x - \frac{9}{2}\right)}^{2} - \frac{81}{4}$
${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$ => ${x}^{2} + b x = {\left(x + \frac{b}{2}\right)}^{2} - {b}^{2} / 4$
Therefore substituting $b = - 9$ we have:
$y = {x}^{2} - 9 x = {\left(x - \frac{9}{2}\right)}^{2} - \frac{81}{4}$