acquiesced

verb: to comply (with); assent (to) without protest,  

Synonyms: submit, agree, accept, approve, yield, bend, surrender, consent, tolerate, comply, give in, conform, succumb, go along with, bow to, cave in (informal), concur, assent, capitulate, accede, play ball (informal), toe the line, 

At first she was totally opposed to the idea of nationwide health care, but after she saw the benefits she finally acquiesced.