The expression $x^2 + 18x - 63$ can be written in the form $(x - a)(x + b)$, where $a$ and $b$ are both nonnegative real numbers. What is the value of $b$?
Factoring, we find that $x^2 + 18x - 63 = (x - 3)(x + 21).$ Therefore, $b = \boxed{21}.$