### Instruction: Find the sum of the real roots of $x^4 - 80x - 36 = 0.$.### Response: To find the sum of the real roots of a polynomial equation, I can use the formula $-\frac{a_{n-1}}{a_n}$, where $a_n$ is the coefficient of the highest degree term and $a_{n-1}$ is the coefficient of the next highest degree term.
In this case, $a_n = 1$ and $a_{n-1} = 0$, since there is no $x^3$ term.
Therefore, the sum of the real roots is $-\frac{0}{1} = 0.$