You can certainly calculate P(55), but where did you get 55 from? Your profit function is a parabola. Since the leading coefficient is negative we know that the parabola has a maximum. (ie it opens downward.) We also know that the maximum value of a parabola is reached when x is on the axis of symmetry of the parabola. How do you find the axis of symmetry?

-Dan

Edit: By the way. You seem to be acting under the assumption that P(55) = 55. It is not. Use a calculator if you are not convinced.