Sure, they were both installed at the same time and they both burned for the same length of time. That is the reason that you want to replace lights in pairs...it is just a matter of time before the second one burns out.
Check your fuses.
sounds like you have a blowen fuse
Yes both headlights can burn out at the same time, I had it happen once, it is rare. If both high and low beams are out, then I would think that it might be the switch. You could get a cheap test light and check the plug to see if there is current to the lights.
Sounds like the high beams are burnt out. Rare that both burnt out at the same time but not impossible.
if both headlights went put it is probably a blown fuse
WIRINGS!!
Replace the slow headlight motor.
From a fuse, No. Each side has a separate fuse. Check for power and ground at the connectors it usually is the light switch or a common wire.
Don't drive at night. Seriously, check the fuses. Headlights usually have their own dedicated fuse that is not on the fuse panel, but instead is usually under the hood inline in the wires running to the lights. Check the owners manual for specific details for your car. It's also possible that both bulbs are burnt out, but that would be unlikely if they both went out at the same time.
Have you checked to see if the brights are not just burnt out? Rarely do they both go at the same time, but it is possible.
No they don't go bad at same time but any smart technician will replace both at same time.
Voltage surge? Bad relay? Bad switch? Bad ground?