<s>[INST] Complete the squares to find the center and radius of the circle I've had trouble on this one problem for a couple days.
Complete the square on the X and Y terms to find the center and radius of the circle.
 $x^2+2x+y^2-4y=-4\:\:$
 [/INST] $$
\begin{align*}
x^2+2x+y^2-4y  &= -4 \\
\Rightarrow x^2+2x+\left( \frac{2}{2} \right)^2+y^2-4y+\left( -\frac{4}{2} \right)^2 &=-4+\left( \frac{2}{2} \right)^2+\left( -\frac{4}{2} \right)^2 \\
\Rightarrow \,\,\,\,\, \,\left(x+\frac{2}{2}\right)^2\quad \,\,\,  +\quad \,\,\,\,\left( y-\frac{4}{2} \right)^2\qquad &= -4+\left( \frac{2}{2} \right)^2+\left( -\frac{4}{2} \right)^2 \ldots
\end{align*} 
$$
Here I have successfully completed the square. I will leave you to clean up the result. Two days is a long time to work with no help, best of luck.
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