Remark
You have to complete the square twice. Begin by transferring the 75 to the right hand side. Put separate brackets around the x terms and another set around the y terms.
(x^2 + 10x ) + (y^2 - 16x ) = - 75
(x^2 + 10x + (10/2)^2 ) + (y^2 - 16x + (16/2)^2) = - 75 + (10/2)^2 + (16/2)^2
(x + 5)^2 + (y - 8)^2 = - 75 + 25 + 64
(x + 5)^2 + (y - 8)^2 = 14
The center is at (-5,8) which is C
Note: The graph is below just to confirm my answer. Notice where the center is and that the radius is just under 4.
