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The phrase "to work out" is correct and usable in written English.
It can be used to refer to solving a problem or puzzle, or exercising. For example: I'm going to the gym to work out for an hour before I head home.
Exact(60)
For you to work out, that one.
Then I tried to work out why.
I had to work out why".
And the numbers have to work out".
"People don't want to work out".
"So I wanted things to work out".
"I'm trying to work out," he said.
It's not hard to work out why.
"I've got to work out," he says.
"I'm going to work out all week.
To work out who he is.
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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