Question

I am trying to find the standard form of this equation for an ellipse.

9x^2 + 4y^2 - 36x + 8y + 31 = 0

First I grouped the x and y's together.

9x^2 - 36x + ? + 4y^2 + 8y + ? = -31 + ? + ?

Then I factored the 9 and 4.

9(x^2-4x+4) + 4(x^2+2x+1) = -31+36+4

9(x-2)^2 + 4(x-1)^2 = 9

Then I divided it all by 9 and got:

(x-2)^2 / 1 + 4(x-1)^2 / 9 = 1

Is this correct or did I mess up somewhere?