From Proto-Italic *gʷīwō, from Proto-Indo-European *gʷíh₃weti (“to live”). The x and c in vīxī and vīctum were introduced by analogy with other verbs.
Cognate with Old English cwic (“alive”) (English quick), Old Church Slavonic жити (žiti), Ancient Greek βίος (bíos), Sanskrit जीवति (jīvati).