First off, I must address Astrokel. The equilibrium constant does not have units.
Now for the real question, you are forgetting to factor in your temperature, try using this formula to solve it: 28.4= [(x/(RT))^2]/[(111/RT)^2*(183/RT)]
Just do some algebra to the formula, plug in the correct value (and units) for R, and then plug in your temperature.
Note, this may not necessarily work, because I believe this equation actually factors in Kc as well.