In beowulf what are the consequences of seeking revenge? what are other ways might problems be worked out?

Beowulf is an epic written about a thousand years back and seeking revenge initiated a clear cycle of revenge as I will explain below.

Grendel the beast gets angry and attacks the Hall killing people, next comes Beowulf who kills Grendel for glory as well as for revenge purposes. Grendel’s mother attacks the kingdom to take revenge and in return killed by Beowulf, making it clear that revenge is a never ending cycle.

Since in Anglo-Saxon tradition the setting of Beowulf, revenge was something held in high esteem, in my opinion any other way would not have seemed successful for the cultural values.