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failed
Describes a plan, project, or attempt that was not successful and did not achieve its goal.
Nach monatelangen Verhandlungen ist der Versuch einer Einigung endgültig gescheitert.
After months of negotiations, the attempt to reach an agreement has definitively failed.
'Gescheitert' (failed) is the past participle of 'scheitern' (to fail). The verb 'scheitern' always forms the past tense with the auxiliary verb 'sein' (to be), because it describes a change of state. So it is always 'etwas ist gescheitert' (something has failed).
Der Plan, das Projekt bis Freitag fertigzustellen, ist leider gescheitert.
The plan to finish the project by Friday has unfortunately failed.
If you want to name the reason for the failure, you use the preposition 'an' followed by the dative. You fail because of something or someone: 'an etwas oder an jemandem scheitern'.
Die Verhandlungen sind am Geld gescheitert.
The negotiations failed because of the money.
It is easy to recognize which meaning is intended: If 'gescheitert' (failed) refers to a thing such as a plan, a project, or a marriage, it is about failure. If it refers directly to a person, it often describes a personal life crisis.
Der Putschversuch ist in den ersten Stunden gescheitert.
The coup attempt failed in the first few hours.
happy / lucky
'glücklich' and 'gescheitert' are opposites when talking about the outcome of a plan, project, or attempt. In this sense, 'glücklich' describes something that was successful and came to a good conclusion. 'gescheitert' means that the goal was not achieved. 'glücklich' sounds positive here and emphasizes the good outcome, while 'gescheitert' clearly says that something did not work.
Der Plan ist gescheitert, weil wichtige Unterlagen gefehlt haben.
The plan failed because important documents were missing.
Nach langer Suche fand das Team eine glückliche Lösung für das Problem.
After a long search, the team found a successful solution to the problem.