When Scott completes the square on the quadratic $x^2 + 8x - 1 = 0$, he obtains an equation of the form $(x + a)^2 = b$.  What is $b$?
The term I need to add and subtract is half of the coefficient of $x$, squared. That is, $(8/2)^2 = 16$. So I rewrite the equation as $(x^2 + 8x + 16) - 16 - 1 = 0$. Now I can factor the parentheses as $(x + 4)^2$, and simplify the rest. I get $(x + 4)^2 = 17$. This is the same as the form $(x + a)^2 = b$, where $a = 4$ and $b = 17$. Therefore, $b = 17$. 