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For this photo, I simply moved in close to the subject (as I wanted a close-up shot of her face), and I took the picture. Since the flash was so close to the subject, the light overpowered her face, resulting in lost detail and "blown out" areas.
For this photo, I simply took a few steps back, and zoomed in with my lens. Increasing the distance between the subject and the flash made the light on her face much more natural looking and appealing.
It's also important to note that flashes also have a maximum effective distance. That's usually around 14 feet for built-in flash units, and it can be much greater for external flash units. That means that when you're photographing your child on stage at a school play, you will need to be within 14 feet (or the effective distance of your flash) to get a properly exposed image using your flash.