Can my marriage work after she cheated while i was deployed?

After some research.. i find out my wife cheated while im deployed. she didnt confess, more like admitted when i pressed her. to my knowledge it happen once, she says because we were arguing and she thougt we weremt going to be together. Ive done way worse things in the past that she doesnt know about, but this hurts soo much because im at war and could die any day. I told her we will work it out when i get home. did i make a bad choice? do my several mistakes trump her one? help me out