problem: For what value of $c$ will the circle with equation $x^2 + 8x + y^2 + 4y + c = 0$ have a radius of length 3?
solution: Completing the square gives us $(x + 4)^2 + (y + 2)^2 = 20 - c$. Since we want the radius to be 3, we must have $20 - c = 3^2$. It follows that $c = \boxed{11}$.