1 : to perform athletic exercises in order to improve your health or physical fitness
She works out at the gym twice a week.
2 a : to happen, develop, or end in a desired or successful way
Our plan worked out perfectly.
We broke up because things didn't work out between us.
2 b : to happen, develop, or end in a particular way or to have a particular result
Despite some difficulties, everything worked out well.
Things don't always work out the way you want them to.
I'm not sure how the story will work out.
How is your new roommate working out? [=how are things going with your new roommate?]
It will work out (to be) cheaper [=it will be cheaper] if we take the bus instead of the train.
With tax, it worked out at/to just over $115. [=the total amount was just over $115]
3 work out (something) or work (something) out a : to find or create (something, such as a solution or a plan) by thinking
I'm trying to work out [=figure out] a way to do it.
We worked out a plan to save money.
We'll work the details out later.
I don't know how you're going to get there. You have to work that out for yourself.
3 work out (something) or work (something) out b : to use mathematics to solve (something)
She worked out the problem on a piece of paper.
4 work (someone) out or work out (someone) British : to understand the behavior of (someone)
He does these crazy things, and I just can't work him out. [=figure him out]