exhaustively
In a way that checks everything very carefully and completely.
Exhaustively means completely and thoroughly, covering every single possibility without leaving anything out. When you search exhaustively for your lost house key, you don't just glance around: you check every pocket, look under every cushion, search through every drawer, and examine every corner where it might possibly be.
Scientists work exhaustively when they test every variable in an experiment. A detective investigates exhaustively by following every lead and interviewing every witness. When your teacher reviews a topic exhaustively before a big test, she makes sure to cover every concept, answer every question, and explain every detail that might appear on the exam.
When you've searched exhaustively, you've checked all the options: there's nowhere left to look. When you've studied exhaustively, you've used every available resource and covered every topic.
Working exhaustively takes serious effort and patience. It's the opposite of a quick scan or a casual once-over. When something matters enough to demand your full attention and you want to be absolutely certain you haven't missed anything, that's when you work exhaustively.