The equation x² - 9x + c = 0 has two real solutions that differ by 5. What is the value of c?

Let the roots be $r$ and $r + 5$. The sum of the roots of $x^2 - 9x + c = 0$ is 9, so $r + (r + 5) = 9$, giving $2r = 4$ and $r = 2$. The roots are 2 and 7. The product of the roots equals $c$, so $c = 2 \times 7 = 14$. Verify: $x^2 - 9x + 14 = (x - 2)(x - 7)$, and $7 - 2 = 5$. A common wrong answer is 20, from using the roots 4 and 5, which sum to 9 but differ by only 1. Another is 9, the sum of the roots, which is the coefficient and not $c$.