Your question is a little unclear, but I will try to suggest:
If the room has a single ethernet cable, then consider adding another wifi router. Give it the same SSID and I believe your devices may automatically select the router they can find, though it may not be the best signal. That depends on the device.
I have a 100Mbps connection, but this "bad room" only gets about 50Mbps are we talking about the wired or the wireless connection here? Sorry, you did say you had a single cable to this room.
My take on a repeater is that the reason why there is a pile of them at Fry's with return stickers is that repeaters are restricted to either broadcast OR receive and cannot do both at the same time. This effectively cuts your bandwidth in half. If you need a repeater, then you really need to cross a very wide river with an island in the middle, for the repeater, because this is the only situation I would choose a repeater for.
If you are getting 50 Mbps per second wifi in the bad room, I would expect the repeater to give you no better.
I am not sure what the ethernet over power solution will do for you, if you have a cable there, as you say.