thoroughly
In a very complete and careful way, without missing anything.
To do something thoroughly means to do it completely and carefully, without leaving anything out or rushing through it. When you clean your room thoroughly, you don't just shove things under the bed. You organize your closet, dust the shelves, vacuum under the furniture, and make sure everything is where it belongs.
A doctor examining a patient works thoroughly, checking all possible causes of symptoms rather than jumping to quick conclusions. A detective investigating a crime scene searches thoroughly for clues, looking in places others might overlook. When a teacher grades papers thoroughly, she reads each answer carefully and provides thoughtful feedback.
The word suggests patience and attention to detail. Someone working thoroughly takes the time to do things right, even when it would be easier to rush. If you study thoroughly for a test, you review all the material, practice the hard problems, and make sure you understand the concepts rather than just memorizing facts.
The opposite of working thoroughly is being careless, superficial, or hasty. When something matters, doing it thoroughly shows respect for the work and for the people who are depending on you.