I believe you meant: Use completing the square to determine the center and radius of the circle represented by this equation: X^2+y^2-10x+6y=15
x^2 - 10x + 25 - 25 + y^2 + 6y + 9 - 9 = 15
Then:
(x-5)^2 + (y+3)^2 = 24 = 2sqrt(6)
This circle is centered at (5,-3) and has radius 2sqrt(6).
