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Wireless charging coupled with computation offloading in edge networks offers a promising solution for realizing power-hungry and computation intensive applications on user devices. We consider a multi-access edge computing (MEC) system with collocated MEC server and base-station/access point, each equipped with a massive MIMO antenna array, supporting multiple users requesting data computation and wireless charging. The goal is to minimize the energy consumption for computation offloading and maximize the received energy at the user from wireless charging. The proposed solution is a novel two-stage algorithm employing nested primal-dual and linear programming techniques to perform data partitioning and time allocation for computation offloading and design the optimal energy beamforming for wireless charging, all within MEC-AP transmit power and latency constraints. Algorithm results show that optimal energy beamforming significantly outperforms other schemes such as isotropic or directed charging without beam power allocation. Compared to binary offloading, data partition in partial offloading leads to lower energy consumption and more charging time, and hence offers better wireless charging performance. The charged energy over an extended period of time both with and without computation offloading can be substantial. Opportunistic wireless charging from MEC-AP thus offers a viable untethered approach for supplying energy to user-devices.