The equation x^2 + 22x + k = (x - r)^2 holds true for all values of x.
To find the sum of r and k, we can compare the coefficients of x in both sides of the equation.
Since the coefficient of x in (x - r)^2 is -2r, and the coefficient of x in x^2 + 22x + k is 22, we can equate them: -2r = 22. Solving for r, we find that r = -11.
Now, substituting r = -11 into the equation x^2 + 22x + k = (x - r)^2, we get x^2 + 22x + k = (x + 11)^2. Expanding the right side, we have x^2 + 22x + k = x^2 + 22x + 121.
Comparing coefficients of x^2, we see that they are equal. Comparing the constant terms, we have k = 121.
Therefore, the sum of r and k is -11 + 121 = 110.
So, the correct answer is B) 110.