ok
you complete the square on the terms in x and y
X2+y2+14x-12y=-69
x^2 + 14x + y^2 - 12y = -69
To complete the square on x^2 + 14x you divide the 14 by 2 to get 7 then you write (x + 7)^2 , now if you expand that you'll get x^2 + 14x + 49 ,which is not x^2 + 14x , of course, so you need to subtract 49 to get back to x^2 + 14x. so we have
x^2 + 14x = (x + 7)^2 - 49
follow?
