soundly
adv.in a way that is very clear, strong, or effective. You use this to describe something that is done well or that has a strong effect.
adv.in a manner that is thorough, effective, or clearly defined. Often used to describe the quality of a victory, a sleep, or a logical argument.
“The team won the game soundly.”
“After a soundly defeating the opposition in the final round, the champion felt confident about her future in the sport.”
“The committee's decision was soundly based on years of empirical research, leaving little room for the critics to challenge the methodology.”
“I realised I would not sleep soundly until I gave in to my body.”
From Middle English soundly, soundely, from Old English ġesundlīċe (“safely, prosperously, gladly”), equivalent to sound + -ly. Originally meaning "safely", the present sense came in the 16ᵗʰ century.
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.