eq = (x - a)^2 + (y - b)^2 + (z - c)^2 - d;
    sol = SolveAlways[{-11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == eq}, {x, y, z}]
    eq /. sol // PolynomialForm[#, TraditionalOrder -> True] &

    (* {{d -> 25, a -> 1, b -> 2, c -> 3}} *)
    (* {(x-1)^2+(y-2)^2+(z-3)^2-25} *)


    eq = (x - a)^2 + (y - b)^2 + (z - c)^2 - d;
    Solve[ForAll[{x, y, z}, -11 - 2 x + x^2 - 4 y + y^2 - 6 z + z^2 == eq], {a, b, c, d}]

    (*{{a -> 1, b -> 2, c -> 3, d -> 25}}*)