This is the 2036th most frequent German word.
nahezu
"Nahezu" means "almost" or "nearly" in English.
In this sentence, 'nahezu' is used to indicate that the solution is almost perfect, emphasizing a small degree of imperfection.
Die Lösung scheint nahezu perfekt zu sein.
The solution seems to be nearly perfect.
Here, 'nahezu' conveys that he has worked for almost all day, implying close to 24 hours but not exactly.
Er hat nahezu den ganzen Tag gearbeitet.
He worked for nearly the whole day.
In this context, 'nahezu' is used to define that almost everyone, but with a slight exception, agreed.