I'm too lazy to figure out the voltage in some formula but I do have that GPU and I went with a 500w PSU. No problems yet. I think one of the problems you will face is that the card is already overclocked out of the box. So as soon as you start pushing your card, you would be trying to push an eighteen wheeler with a little four cylinder car.
If I was a betting man and were to bet on your system lasting with that 350W PSU, then I would bet your system wouldn't last long. But hey, what do I know.
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