When you have a problem involving a leaky faucet and you fix the faucet, this is an example of when you resolve your problem.
When you settle an old argument you have been having, this is an example of when you resolve the argument.
When you vow to exercise more, this is an example of when you resolve to exercise more.
Resolved the problem.
Resolve a conflict.
My resentment resolved itself into resignation.
Resolve on a course of action.
A discussion that resolved itself into an argument.
The flood that resolved him to sell.
To resolve to go.
To resolve a riddle.
He was resolved by an unexpected event.