A uniform beam AB AB\,AB has length 8 m and mass 20 kg. It rests horizontally on two supports at C C\,C and DDD, where AC=2AC=2AC=2 m and AD=6AD=6AD=6 m. A crate of mass 30 kg is placed on the beam with its centre of mass x x\,x m from AAA.
Find the set of possible values of x x\,x for which the beam remains in equilibrium on both supports.