jmc

Dividing both sides of the equation $11x^2-44x-99$ by $11$, we have $$x^2-4x-9=0.$$The square which agrees with $x^2-4x-9$ except for the constant term is $(x-2{)}^2$, which is equal to $x^2-4x+4$ and thus to $(x^2-4x-9)+13$.

Therefore, by adding $13$ to each side, Krzysztof rewrote the equation $x^2-4x-9=0$ as $$(x-2{)}^2=13$$We have $r=-2$, $s=13$, and thus $r+s=\boxed{11}$.