The graphs of y = x² and y = 3x + 4 intersect at two points. What is the sum of the x-coordinates of these two points?

Set the two expressions equal: $x^2 = 3x + 4$, which becomes $x^2 - 3x - 4 = 0$. The $x$-coordinates of the intersections are the roots of this quadratic. By Vieta's formulas, the sum of the roots is the negative of the $x$-coefficient divided by the leading coefficient: $-(-3) = 3$. Factoring confirms it: $(x-4)(x+1) = 0$, so the roots are 4 and $-1$, which sum to 3. A common wrong answer is $-3$, from forgetting to flip the sign, and another is $-4$, which is the product of the roots.