Solving for V and I in a diode circuit by making assumptions

Question

I want to make sure I understand the solution to this problem from my textbook. The goal is to solve for V and I in the circuit below:

They start by assuming that both diodes are conducting and solve for V and I. After solving the circuit, a negative value for I was obtained. They said this was not possible, and then they restarted the problem with a different assumption.

From my understanding, it is not possible for I to be negative because that would mean I goes in the opposite direction; if I went in the opposite direction, the diode would not be forward biased as was assumed, so there is a contradiction. Is that the right idea?

Answer 1

if I went in the opposite direction, the diode would not be forward biased as was assumed, so there is a contradiction. Is that the right idea?

Yes. This is a better way to think of it than to say the solution is "impossible".

The solution contradicted one of the assumptions made to reach the solution. Therefore it is not a self-consistent solution, and you should try a different set of assumptions until you find one that gives a self-consistent result.