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朝食を済ませて

finish breakfast

→ 朝食
phrase Rare #34,311
finish breakfast 済ませる means to finish or get something done; 朝食を済ませて is the te-form, linking the completed breakfast to what follows.
JA: 朝食を済ませて、学校へ行きました。
EN: I finished breakfast and went to school.

遅い朝食を済ませて、ちょっと釣りをしてるところだ。

I had a late breakfast, and now I’m doing a little fishing.

私はまだ朝食を済ませていません。

I haven’t had breakfast yet.