Find the center and the radius of the circle with the equation x^2+2x+y^2-2y-14=0

The standard form of a circle is (x-h) ² + (y-k) ²=r², (h, k) is the center of the circle, r is the radius.

x²+2x+y²-2y-14=0

make squares by adding (half of b) squared: the "b" for x is 2, the "b" for y is "-2" in this case, so add 1 to each, then subtract 1:

x²+2x+1+y²-2y+1-1-1-14=0

(x+1) ² + (y-1) ²=4²

so the center is at (-1,1) and the radius is 4.