TP-Link AC1750 Universal Dual Band Range Extender

I have a 15 meter ethernet cable going to a room in my house out of wifi range of my router. This serves a tv and disc player via a splitter box with spare port available for another ethernet cable. Since the AC1750 has an ethernet port on its side it occurred to me that perhaps I could wire the two together and get perfect wifi for my wireless devices in that room? The alternative is to place the extender in a position half way between my router and the far room. Ive tried that but the wifi signal is poor due to walls and distance. No good...

Please advise...