I have an odd problem in my book that i am trying to solve but dont have the solution to.

Can anyone help me?

Find the center and radius of the sphere whose equation is:

$\displaystyle x^2 + 2x +y^2 - y + z^2 = 0$

Attempt:

$\displaystyle (x^2 + 2x + 1) -1 (y^2 - y - 1/4) + 1/4 + z^2 = 0 $

$\displaystyle (x^2+1)^2 + ( y^2 - 1/2)^2 + z^2 = 1 - 1/4 = 3/4$

r = $\displaystyle r^2 = 3/4$

r=$\displaystyle \sqrt {3/4}$

radius: $\displaystyle 2 \sqrt {3}$

Center: $\displaystyle (-1, + 1/2, 0)$

Am i correct?