HMMT-Feb 2019 guts, Problem 1

Find the sum of all real solutions to $x^{2}+\cos x=2019$.

Solution: The left-hand side is an even function, hence for each $x$ that solves the equation, $-x$ will also be a solution. Pairing the solutions up in this way, we get that the sum must be 0 . $\fbox{0}$.

Answer: 0