Plug is broken at attachment point of device

Hi Lucy,

That's a fairly standard 3.5mm audio plug, although it's got three rings and a tip so it'll be marginally more difficult to find a replacement, but certainly not hard by any means.

That means there are at least four wires going to the plug, and you'll have to identify which wire goes to which band/tip on the plug in order to get it rewired to work correctly. In the spirit of iFixit, we'll be happy to try and help you do that, but first let me suggest an alternative.

Since the cord is completely detachable from the headphones, it makes a certain amount of sense that it might be available separately, and indeed, that turns out to be the case. I just did a quick search on Amazon and several cords came up that should all work; here's a representative sample that specifically says it will work with your headphones.

Amazon.com: Mr Rex Replacement Audio Cable Cord with Mic for Bose 700 QuietComfort QC35 QC35II QC25 QC45 Headphones, JBL E45BT E55BT E65BTNC 750NC Earphone, Nylon-Braided 2.5mm to 3.5mm Aux Cord Wire(1-Pack, 5ft) : Electronics

You can also check places like eBay and AliExpress where you may be able to find the parts even cheaper if that's a concern.

I present that as a labor-saving opportunity, but fully support you if you want to go ahead and try and repair your existing cord. Let us know and we'll see if we can go about finding a replacement and figuring out how to wire it up.