Completing the square

The graph of the equation
$$x^2-2 x+y^2+4 y = 4$$
is a circle. Find the center and radius of that circle.

• edited January 17

We can start by writing out our equation like so:
$x^2 - 2x +(-1)^2 - (-1)^2 + y^2 + 4y + 2^2 - 2^2 = 4$

From there we can clean it up a bit
$x^2 - 2x +1 -1 + y^2 + 4y + 4 - 4 = 4$

And then do some factoring
$(x-1)^2-1 + (y+2)^2 - 4 = 4$

And add the constant terms over
$(x-1)^2 + (y+2)^2 = 9$

And voila this equation tells us that the circle is centered at (1,-2) with a radius of 3.