Hi, As mentioned previously you do not want to do one subwoofer, two is the minimum.
You have smaller bookshelf speakers hopefully on stands. These speakers have the ability to perform acceptably in a room that large , but it is pushing it. In order to get satisfactory headroom you are going to have to remove 100 Hz on down from them and hand it to two subwoofers at least 12" in diameter (the drivers) via a two way crossover. The best are digital such as the MiniDSP or dBx Driverack.
If you are handy the least expensive way to get started in subwoofers is to build them yourself from kits such as those sold by Parts Express. They even have a selection of excellent plate amplifiers although I prefer outboard amps for subwoofers. QSC makes excellent amps for subwoofers at very reasonable prices. You can get two subs, amps and crossover for less than you could buy a single high quality 12" subwoofer from JL Audio.
If you go with one subwoofer using a low pass filter you will be very disappointed in a 400 square foot room.