+129852
x^2 + 10x + y^2 + 12y + 52 = 0 subtract 52 from both sides
x^2 + 10x + y^2 + 12y = -52
Complete the square on x.....take (1/2) of 10 = 5....square it = 25, add it to both sides
x^2 + 10x + 25 + y ^2 + 12y = -52 + 25
Complete the square on y....take (1/2) of 12 = 6....square it = 36, add it to both sides
(x^2 + 10x + 25) +( y^2 + 12y + 36) = -52 + 25 + 36
Factor the stuff in parentheses- both will be perfect square trinomials ....simplify the right side
(x + 5)^2 + ( y + 6)^2 = 9
