Given is the following equation of a circle, for which I've to determine its centre and radius. I'm running into some difficulties when I'm trying to complete the squares.

$\displaystyle x^2 + y^2 -2x + 4y = 4 \Leftrightarrow (x - 1)^2 + (y + 2)^2 = 4$

This leads me to believe the centre would be (1, -2). Now to find its radius I'll just complete the squares and simplify:

$\displaystyle (x - 1)^2 + (y + 2)^2 = 4 \Leftrightarrow x^2 - 2x + 1 + y^2 + 4y + 4 = 4 \Leftrightarrow x^2 - 2x + y^2 + 4y = -1$

This obviously isn't correct, -1 being kind of a weird radius

. So what am I doing wrong here? The correct answer (according to my textbook) should be r=3. I guess I'm missing something with completing the y-part, since -1 + 4 = 3, but can't wrap my head around it...

Any handy tips for solving these kind of exercises?