。
Keiko and Ichirou broke up by mutual consent.
Literal
Keiko [and-と] Ichirou [subj-が] mutual-agreement-[by-ずくで] separated.
納得ずく 'by mutual consent / with full agreement' uses the suffix ずく (variant: づく) meaning 'on the basis of / with full X' — similar to 金ずく 'by force of money.' 別れた is the past of 別れる 'to separate/break up.' A terse, matter-of-fact narrative statement.