# How do you complete the square for x^2 + 11x?

Jul 19, 2015

${x}^{2} + 11 x = {\left(x + \frac{11}{2}\right)}^{2} - {11}^{2} / \left({2}^{2}\right) = {\left(x + \frac{11}{2}\right)}^{2} - \frac{121}{4}$

#### Explanation:

In general,

$a {x}^{2} + b x + c = a {\left(x + \frac{b}{2 a}\right)}^{2} + \left(c - {b}^{2} / \left(4 a\right)\right)$

Notice the $\frac{b}{2 a}$ term.

In our case $a = 1$ and $b = 11$ hence the $\frac{11}{2}$