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I'm not sure if you're aware of this but your RCA set does not have BlueTooth in any sense, it is simply not built into the TV. In fact, less than 5% of high end TV's produced (upper end LG and Samsung sets) use BlueTooth for anything other than connection to a keyboard or mouse.
If you're looking to connect the speaker to the set, you'll need to us an alternative connection, OR you can purchase adapters for the set so that you CAN connect the speaker to the TV via BlueTooth.
This TV use a headphone out, and a digital audio out for connection to a speaker. The easiest way to connect a BlueTooth transmitter to the TV is using the headphone jack out, and then purchasing and connecting the BlueTooth transmitter at the link below to the set:
Then you simply pair the speaker to the BlueTooth transmitter and the TV sound will come through the speaker.
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