The real world isn't always so cooperative. However, a simplified lighting solution can still work in many cases.

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A single light placed in the traditional key light position can be used with a reflector in the position of the usual fill light. This setup provides proper exposure from the main light and the reflected light prevents dark shadows being cast by the subject's nose or other facial features. Another possibility is to try and make the key light less harsh using an umbrella or softbox. All that is left is to prevent any shadow from appearing in the background of the portrait.
To avoid a shadow behind the subject, you can either move the subject further away from the background or increase the angle of the light. In a large room, it is best to move the subject out from the background. The further away from the background, the lower the subject's shadow will be. For a portrait focused on the head and face, only a small amount of separation may be necessary. Remember, there is no need to eliminate the shadow altogether, merely to relocate it out of the frame.
If the subject cannot be moved a suitable distance from the background, then the shadow can be eliminated by increasing the angle at which the main light is to the subject's face. Doing so throws the shadow further and further to the subject's side until a composition can be created in which there is no shadow in the shot. Unfortunately, increasing the angle increases the intensity of light required from the fill light, so a tradeoff exists.