I'm a student and I need help with this circuit analysis.

So I know those are the right answers to voltage going in that direction over v1 and v2 because this was an in class exercise and I recreated the circuit on a simulator. What I couldn't figure out from class or at home yet is how to do the calculations correct, especially for the -5.88v going over v2. I think Rtotal should be 7.727ohms and I think that's what we said it was in class but after that I'm lost and it didn't help that the teacher explaining it to us was sick lol! God I hate the traditional classroom and lab structure for this stuff but that's another discussion.

So if I take out the 25v battery, the resistance total I thought should still be the same and then I would calculate 10volts divided by Rt 7.727ohms which should be 1.29amps current total, after that I'm kinda lost though.

 

Yes , Rtot is indeed equal to 7.72Ω
Also, notice that we can find V1 without doing almost any calculations.
Do you know that the voltage is a potential difference bettwin two points?
What is the voltage at the most left node? And what is the voltage at the most right node? With respect to ground.

I know that this is not so obvious to you but you can remove the top 10 Ohms resistor from the circuit and still be able to find the V2 voltage.

 

Ah, I think I'm starting to understand this a lot better now and can solve the circuit and get the right answers. Thank you sooo much!