42Circle, completing the square

Find the centre and radius of the circle $\displaystyle x^2 + y^2 - 6x + 4y - 12 = 0$.

The circle has centre (3, −2) and radius 5. Completing the square turns x² + y² − 6x + 4y − 12 = 0 into (x−3)² + (y+2)² = 25, matching (x−h)² + (y−k)² = r². Check: 9 + 4 − 25 = −12 ✓.