If $a \clubsuit b = a^2 + 2ab + b^2$ and $2 \clubsuit x = 81$, find the sum of all possible values of $x$.
I notice that the expression $a^2 + 2ab + b^2$ is the same as $(a + b)^2$. So I can rewrite $a \clubsuit b$ as $(a + b)^2$. Then $2 \clubsuit x$ is just $(2 + x)^2$. If $(2 + x)^2 = 81$, then I can take the square root of both sides and get $2 + x = \pm 9$. So $x$ can be either $7$ or $-11$. The sum of these two values is $7 + (-11) = -4$. 