2x2 + 8x + (____) + 2y2 - 12y + (____) = 24 Then divide through by the coefficients of the two squared terms. You're trying to make this look like the equation for a circle which has the two square binomials set equal to the radius. Anyway, since both coefficients are 2, simply divide the whole thing by two. x2 + 4x + (____) + y2 - 6y + (____) = 12 Now look at the x term, 4x. Take half of the coefficient (4/2 = 2) and square it (which brings us back to 4, coincidentally) and add that to both sides. Do the same for the Y term. Write it like this to show clearly what you've done: x2 + 4x + (4) + y2 - 6y + (9) = 12 + 4 + 9 Now factor your two perfect square trinomials and add up all the loose numbers on the right. (x + 2)2 + (y - 3)2 = 52 (Turned the 25 into 5-squared for the next step. You should do this too) This looks like: (x - h)2 + (y - k)2 = r2 You should be able to pull the correct center coordinates and radius from there.