Find the center and radius of 2x^2+2y^2-8x+10y+2=0

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.