The given equation is `x^2+22x+k=(x-r)^2`. Expanding the right side of the equation, we get `x^2+22x+k=x^2-2rx+r^2`. By comparing the coefficients of like terms on both sides, we can see that `22=-2r`, which implies that `r=-11`. Substituting this value of `r` into the equation, we get `k=r^2=(-11)^2=121`. Therefore, the value of the sum `r+k` is `-11+121=110`. So, for all values of `x`, the value of the sum `r+k` is **110**. Is there anything else you would like to know?