0 to do a calculation to get an answer to a mathematical question -- 計算出
1 to understand something or to find the answer to something by thinking about it -- 理解;想出
[ + question word ] There will be a full investigation to work out what caused the accident. 將進行全面的調查,以找出事故發生的原因。
[ + that ] Investigators needed several months to work out that a fraud had been committed. 調查人員需要幾個月的時間才能查出欺詐行為。
2 If a problem or difficult situation works out, it gradually becomes better or satisfactory, and if you work it out, you make it better or satisfactory. -- (使)好轉,(使)出現轉機
When we worked out how much it cost us to run a car, we decided to sell it.
I couldn't work out what was going on.
I couldn't work out what his expression meant.