1To finish, end, or be completed; to be resolved (intransitive).
手続きはもう済みましたか？
Have the procedures been completed already?
宿題が済んだら遊びに行っていいよ。
You can go out to play once your homework is done.
会議は予定どおりに済んだ。
The meeting finished as scheduled.
2To have a less severe result than expected; to get off lightly (damage or harm is limited).
事故の割にはけがが軽く済んだ。
Considering the accident, the injuries were minor.
今日は雨で済んだからラッキーだった。
We were lucky that it only rained (and nothing worse happened).
3To be satisfactory so that one can feel at ease; to be enough to settle the matter.
謝ればこれで済む問題ではないが、まず謝るべきだ。
This isn't something that can be settled just by apologizing, but you should apologize first.
それで済むなら、早くそうしてしまおう。
If that'll do, let's just do it quickly.
4Used (often in negative forms) to express unease, guilt, or regret about troubling someone (e.g., 'to feel sorry' or 'not to be satisfied').
手伝ってもらってばかりで済まないと思っている。
I feel bad/I'm sorry for always having people help me.
言い過ぎて済まないとも思っているが、言わなければならなかった。
I regret that I may have gone too far with my words, but I had to say it.