The team announced on Wednesday the former Manchester City man will miss 8-10 weeks with three fractured lumbar vertebrae. No surgery will be required.
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Boateng landed hard on his back after challenging for a header with Real Salt Lake's RSL midfielder Luke Mulholland.
"This is unfortunate timing for Nana," Rapids sporting director Padraig Smith said. "He has acclimated quickly to the team and the altitude, and was beginning to show the talent and forward drive we identified when bringing him to the club."