work out
With or without an object
Solve a problem or calculate an answer
I cannot work out the answer to question five.
Do physical exercise (no object)
He works out at the gym three times a week.
With or without an object
It can be used with no object, and it can also take one. With an object it is usually separable: turn the volume up, turn it up.
The particle: out
This verb belongs to the group ‘finding an answer’.
Others in the group: find out, figure out.
Practise it
Add it to your daily practice or see every verb with out.
Further reading: work out on Wiktionary (CC BY-SA).