Your solution (however wrong) seems to be a bit convoluted.
Look at it simply.
First, group your x and y, and move +36 to the right side.
The trick here is to add a constant to the x and y group that will make the resulting trinomial a perfect square.
How do we do that?
Take half of the coefficient of the linear term, square it, then add it to the group. Do that for both the x and y group. And since we added a certain amount to the left side, we must add that same amount to the right side.
So, here we go.
Half of -10 is -5. We square that to get 25 and we add that to the x group to get .
Half of 8 is 4. We square that to get 16 and we add that to the y group to get .
We added a total of 25 + 16 on the left, so we add that amount to the right to keep things balanced.
Finally, grouping the two perfect square trinomials, we arrive at
Center (5, -4), Radius =