We know that $ (ax + b)^2 + c = (a^2)x^2 + (2ab)x + b^2 + c, $ meaning that if this to equal $ x^2 - 8x - 49 $, we start with $ a^2 = 1, $ and so we let $ a = 1 $. Then, $ 2ab = -8, $ so $ b = -4 $. We do not need to find $ c $ in this case, so our answer is $ ab = \boxed{-4} $. Note: Letting $ a = -1 $ gives us $ (-x+4)^2 + c, $ which gives us the same answer.