Any time you point a light at a subject, shadows and highlights will result. Use a reflector or a supplemental light to lighten (but not eliminate) the shadows. Your goal is to show detail where it would otherwise be dark. Technically, you should create a lighting ratio between 1:2 and 1:3 between the highlight and shadow portions of the image.

You need shadows to create the illusion of depth in the image. If you eliminate them completely, the subject will appear flat and lifeless. You have a driver's license photo, don't you?