What is the sum of all values of x that satisfy 2^x²-5x = 2^-6?

Both sides have base 2, so the exponents must be equal: $x^2 - 5x = -6$. Move everything to one side: $x^2 - 5x + 6 = 0$, which factors as $(x - 2)(x - 3) = 0$. The solutions are $x = 2$ and $x = 3$, and their sum is $5$. You can also read the sum directly from the equation: for $x^2 - 5x + 6 = 0$, the sum of the roots is $-(-5) = 5$. Common wrong answers include 6, which is the product of the roots, and $-5$, which comes from forgetting that the sum of roots is the opposite of the $x$-coefficient.