# How do you complete the square for #x^2 + 9?

May 24, 2015

Since ${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$

If ${x}^{2}$ and $\left(+ 9\right)$ are two terms of an expression of an expansion of the form ${\left(x + a\right)}^{2}$
then
$a = \pm 3$

and there are 2 possible ways of "completing the square"

${x}^{2} + 9 = {\left(x + 3\right)}^{2} - 6 x$
or
${x}^{2} + 9 = {\left(x - 3\right)}^{2} + 6 x$