What is the sum of all possible values of $x$ such that $2x(x-10)=-50$?
First, I can simplify the equation by dividing both sides by $2$, which gives me $x(x-10)=-25$. Next, I can expand the left side by multiplying out the parentheses, which gives me $x^2-10x=-25$. Then, I can move everything to one side and make it equal to zero, which gives me $x^2-10x+25=0$. Now, I have a quadratic equation in standard form, and I can try to factor it. I look for two numbers that multiply to $25$ and add to $-10$. I can see that $-5$ and $-5$ work, so I can write $x^2-10x+25=(x-5)(x-5)$. Therefore, the equation is equivalent to $(x-5)^2=0$. This means that the only value of $x$ that satisfies the equation is $x=5$. So, the sum of all possible values of $x$ is just $5$. 