jmc

The only time this expression is not defined is when the denominator is equal to 0. In other words, we are looking for all solutions to the equation $x^2-20x+100=0$. We can find the roots by factoring the quadratic into $(x-10)(x-10)=0$ or by using the quadratic formula: $$x=\frac{20\pm \sqrt{(-20{)}^2-4(1)(100)}}{2}.$$ Either way, we see that $x=10$ is the only time when the denominator of our expression is equal to 0. Therefore, our answer is $\boxed{10}$.