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"working this out" is correct and usable in written English.
You can use it whenever you're trying to figure something out or solve a problem. Example: I'm not sure how to proceed with this problem, so I'm going to try working this out.
Exact(27)
We're in the early days of working this out".
"I look forward to the court system working this out rather than through the media".
It's not just a question of working this out in space.
"It took a long time working this out," said Cyrus M. Schindler, the nation's president, who joined Mr. Pataki at the news conference.
However, according to Geoff Harvey's book Successful Football Betting, it is almost impossible to handle the data involved in working this out fairly.
"Or," I said -- I always tried to give my students an "or" -- you could not hit me, and we could get together at lunch and maybe there would be some other way of working this out".
Similar(32)
"We've worked this out," she said.
He wanted to work this out".
You may have worked this out already.
"Elliot and I will work this out".
We have to try to work this out together.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com