Quadratic by factoring

Statement

Solve the equation $x^2 - 11x + 24 = 0$.

Solution

Look for two numbers with sum $11$ and product $24$: they are $3$ and $8$. Hence $x^2 - 11x + 24 = (x-3)(x-8) = 0,$ so $x = 3$ or $x = 8$. Check: $3^2 - 11\cdot3 + 24 = 9-33+24 = 0$ and $8^2 - 11\cdot8 + 24 = 64-88+24 = 0$. Correct. $\boxed{x = 3 \ \vee\ x = 8}$