了却的英文：
finish; settle; solve

参考例句：

That has lifted a load from my mind.
那使我了却了一桩心事。

We were down to10 gallons and we still had a long way to go.
我们只剩下10加仑油了却还有那么长的一段路要赶。

finish是什么意思：
v.
1.结束，完成（某事物）；达到工作或活动的结束阶段
2.[~ sth (off/up)]把所剩之物吃完、喝完或用完
3.[~ sth (off)]完成某事物、使某事物臻于完美， 加工
4.[~ sb (off)]【口】使某人筋疲力尽
5.[~ sb (off) ]【口】毁坏某人、某事物；与某人断绝关系，终止与某事物的联系
n.
1.[C]某事物的最于部分或结尾
2.[C, U]完成的或完美的状态
3.[C] 用于处理木器等表面的方法、材料或物质

Finishing touches
收尾工作

It was an exciting finish.
比赛结尾是激动人心的。

Are you finished with the scissors?
你用完剪刀了吗？

settle是什么意思：
v. （使）定居，安定；解决；安排；沉淀；下陷

It was settled by lot.
这事是以抽签决定的。

It was settled by lotting.
这事是以抽签决定的。

No question is ever settled until it is settled right
正确解决问题才算真正解决

solve是什么意思：
v. 解决；破解

Will you help me to solve this twister?
你能帮助我解决这个难题吗？

I just solved the mystery.
我刚刚把那个谜底解开了。

It was a physical problem that had to be solved.
要解决的问题是个实际问题。