problem: If $a \clubsuit b = a^2 + 2ab + b^2$ and $2 \clubsuit x = 81$, find the sum of all possible values of $x$.
solution: We can see that $2\clubsuit x = 2^2 + 2\cdot 2\cdot x + x^2 = 81$. This becomes a quadratic: $x^2 + 4x - 77 = (x + 11)(x - 7) = 0$. Thus, $x = 7, -11$ and our answer is $\boxed{-4}$.
  
  - OR -
  
  We note that $a \clubsuit b = (a + b)^2$. Thus, $(2 + x)^2 = 81$. It follows that $2 + x = 9$ or $2 + x = -9$, leaving us with $x = 7, -11$. We find that the answer is $\boxed{-4}$.