If they know you will fix it, they feel they have accomplished something and that their dissatisfaction has not been in vain. In fact, this last point is crucial. Turning what starts out as a guest complaint into an actual guest compliment is a real art, but it can be done more often than you d think. A guest who knows he has been heard, really listened to, and whose advise has been taken is a happy guest. Some of my most favorable guest compliments had begun life as a guest complaint.
Body language is crucial.
There is no one right answer here. In short, you learn to read people. Above all, be on their side and not against them. This is the crucial non-quantifiable element to a good handling of a guest complaint. Do not phrase it as an us vs. them situation.