x² - 10x + y² + 8y = 28

Take one-half the -10, which is -5
Square -5. Get +25
Add +25 to both sides, putting it right after the -10x on the left

x² - 10x + 25 + y² + 8y = 28 + 25

Take one-half the +8, which is +4
Square +4. Get +16
Add +16 to both sides, putting it right after the 8y on the left
 
x² - 10x + 25 + y² + 8y + 16 = 28 + 25 + 16

Combine the terms on the right

x² - 10x + 25 + y² + 8y + 16 = 69

Factor the first three terms on the left as (x - 5)(x - 5) and 
then write it as (x - 5)²

(x - 5)² + y² + 8y + 16 = 69

Factor the last three terms on the left as (y + 4)(y + 4) and 
then write it as (y + 4)²

(x - 5)² + (y + 4)² = 69

Compare to 

(x - h)² + (y - k)² = r²

Then 

-h = -5 so h = 5 

-k = +4 so k = -4

So center = (h,k) = (5,-4)
                 __
r² = 69, so r = Ö69

Edwin