First, the "right" way to do this derivation, as I see it, is to first do it with center at the origin, and then just do a transformation to shift it to another center. There is no reason for force anyone to do it the hard way! (I suppose doing it once in your life, to practice perseverance, can be of use ...)
In your work, I see a sign error or two (next to last line). You also failed to square the 2 on the left.
Check carefully for such details, and just continue (isolate the radical on one side again, square, and so on). Your work at the origin should serve as something of a template for this work, knowing that in the end you should have (x-h) and (y-k) where x and y are.
Just keep at it; if you continue to be stuck, try telling us what it is that you want to do next, and why you think you can't. You may discover an error for yourself; at least it will help others see what to tell you, beyond my advice to persevere.
