B737 Captain reported engine failure on takeoff. The flight crew rejected the takeoff and returned to the gate for maintenance action.

Narrative

Normal ZZZ takeoff. Loud bang and accompanying yaw to the right at approximately 80 kts. Initially believed it was a tire failure. Rejected the takeoff; maintained directional control; and eased it to a stop with a tire failure possibility in mind. Assessed that we had an engine failure. Made the PA to remain seated and that we'll be right back with you. Assessed that there was no fire and cleared the runway to the right at Taxiway 1 and requested the fire trucks to inspect the aircraft. Had the First Officer pull out the QRH for an engine failure; while I spoke to the Flight Attendant who said that all passengers were calm and confirmed no fire indications or fumes in the cabin. Performed the engine failure QRH. Ran brake cooling performance; which showed no restrictions. Fire informed us that the aircraft inspected well; no tire indications; brake temperatures indicated 170 degrees; and that they had no issue with us taxiing to a gate. Tower asked if we could move forward on Taxiway 2 and informed us that they did find shrapnel on the runway during their inspection.Coordinated with fire and did move forward onto [Taxiway] 2. I then called Dispatch who connected us to the Chief Pilot. I went over what happened with the Chief Pilot while the First Officer communicated with ZZZ Ops for a gate. The Chief Pilot agreed that we should taxi to the gate; which we did. Gate XX. Fire escorted us to the gate where medics also met us in the jet way to assess any panic or medical issues with passengers. Passengers were in general good spirits. I did try and greet as many as I could and ask if they were okay; especially those with children. All responded yes. ZZZ Manager and Supervisors were there to make sure all crew and passengers were okay. Called the Supervisor and asked if we should terminate and allow Ramp to move the aircraft and they said yes. Terminated aircraft normally.