Formula for completing the square? My math teacher said that this was the formula for completing the square.
Original function: $$ax^2 + bx + c$$
Completed square: $$a\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a} + c$$
However, using this formula I'm not getting the same answers that I would get just by determining the stuff myself.  Is this correct?

Note that
$$\begin{align*}a\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a} + c&=a\left(x^2+2\left(\frac{b}{2a}\right)x+\left(\frac{b}{2a}\right)^2\right)- \frac{b^2}{4a} + c\\ &=a\left(x^2+\left(\frac{b}{a}\right)x+\frac{b^2}{4a^2}\right)- \frac{b^2}{4a} + c\\ 
&=\left(ax^2+bx+\frac{b^2}{4a}\right)- \frac{b^2}{4a} + c\\\\
&= ax^2+bx+c \end{align*}$$
so the formula is correct. Try plugging in the numbers $a$, $b$, and $c$ you are using to each step here and seeing where they begin to differ; that will be where your error is.
