For  2x^2 + 2y^2 + 3x - 5y + 1 = 0. First we divide 2 everywhere, yields,
x^2 + (3/2)x + y^2 - (5/2)y = -1/2.
(x + 3/4)^2 + (y - 5/4)^2 = -1/2 + 9/16 + 25/16 = 26/16.

This represent a circle, centered (-3/4, 5/4) and radius sqrt(26)/4.