Room remodel with new subfloor

Am currently involved in a second floor bathroom remodel project where I have removed the entire subfloor. I'm ready to install the new subfloor, but am wondering how best to handle the sides of the room that run parallel to the floor joists. There are no joists that line up exactly with each end of the room and I'm trying to figure out the best way to support the new subfloor since I don't want to leave those ends floating. Any suggestions on how to handle this?
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SteveG

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SteveG wrote:

If the existing joists are close to where you need them nail a 2x4 to the existing joist to support the plywood. If the are too far away for that cut some blocking to install perpindicular to the joists to support the subfloor.
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