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From English - German Ding/FreeDict dictionary ver. 1.9-fd1 : [ freedict:eng-deu ]
reasoned out /ɹˈiːzənd ˈaʊt/
herausgefunden, ausgeknobelt, ausgerechnet
Synonym: figured out
see: figure out sth., reason out sth., figuring out, reasoning out, figure out a math problem