Hi and welcome to Just Answer. I'm sorry to hear about your TV. I will try my best to give you a precise and accurate answer.
This model has a headphone jack. You can use that to output an analog audio signal.
What kind of speakers are you planning to use? Are they self powered?
Let me know and I'll complete my answer.
Ok, so you need something to power the speakers.
You would need to buy a cheap receiver, maybe a used one. Best Buy has some for $229: http://www.bestbuy.com/site/Pioneer+-+400W+5.1-Ch.+3D+Pass+Through+A/V+Home+Theater+Receiver/9846483.p?id=1218183107289&skuId=9846483
Here's how its done.
The TV has an optical audio output (like all most new TVs). You simply run an optical cable from the TV to the receiver.
Or, if you buy a cheap receiver with no optical input, you can use the headphone jack and purchase a 3.5mm to RCA adapter like this one: http://www.amazon.com/gp/product/B0016LTZFI/ref=pd_lpo_k2_dp_sr_2?pf_rd_p=486539851&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=B000A3GPIS&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=1J9TKY0N1V0N0M0HC7CC
Does that make sense? Let me know.
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They are not recievers. They are 2 Awia 150 watt sterio speakers. There is only one earohone jack. How would I connect two speakers to that?
Can I run optical audio output cables from the TV directly to my speakers? If so, please give me specifications and size for the cable.
You can't use speakers without amplification unless they are self powered.
You need an amplifier or receiver of some kind between the TV and the speakers.
On the back of the speakers are there any kind of connections other than the speaker wire terminals? If the answer is 'no' then the speakers are 'regular' speakers and need amplification.
Check for me.