The equation x² - 15x + c = 0 has two real solutions that differ by 7. What is the value of c?

Let the roots be $r$ and $r + 7$. For $x^2 - 15x + c = 0$, the roots sum to 15, so $2r + 7 = 15$ and $r = 4$. The roots are 4 and 11, and $c$ is their product: $4 \times 11 = 44$. Check: $x^2 - 15x + 44 = (x - 4)(x - 11)$, and $11 - 4 = 7$. A common wrong answer is 56, from using the roots 7 and 8, which sum to 15 but differ by only 1. Another is 15, the sum of the roots, which is the $x$-coefficient and not $c$. A third is 7, the difference.