What should I do with this begonia?

I am overwintering some begonias for a friend.

The one in the pic had powdery mildew and I gave it a few sprays of baking powder mix(baking soda? dont remember which now!) and that seemed to control it. However many of the leaves are drying out starting at the edges. Also there is a very long stem ( somewhat like I have seen on African Violets ) and I am wondering what is best to do with this - especially since it is not mine! Just clip off the leaves that are drying or cut back the stem and let new growth come up and root the stem I cut off? Not sure how but seems to me that can easily be done?

Even in our very humid climate in south Texas.........I have to put begonias under glass of some kind.........I use everything from take out big big salad bowls to make terrariums for them........there is just not enough humidity in the house to keep them happy............

Definitely looks pretty dry. Cut off all of that dead foliage. Keep it moist and it will come back.

I do keep the roots moist that is not a problem.

Humidity of course may be although the other 3 I have are looking fine.

Begoniadude............would it do any good to mist the leaves several times a day???? I might start trying that when I am forced to bring them in................

I am not sure about misting. If a Begonia is that fussy I usually get rid of it. ; )

So now I just need an answer to the other questions.
Can I cut back the long stem and root it - and if so what medium is best.

Yes - you can root the leaf. Experiment with different mediums. I prefer water rooting but do what works for you.