Blow dried, Blew dried, blowed dry, blew dry, So which is it?

So as I sat in class and was looking at a list of pet peeves, the whole list got me thinking. How do you really say that you have dried your hair past tense with the word blow. Is it 'blow dried', 'blew dried', 'blowed dry', or 'blew dry'? I know I am not the only one who has had conversations that you are about to say "I blow dried my hair" you stop and say it three times trying to figure out which one is the correct way to say it. Then there is that moment where everyone your talking to is trying to figure it out too and it ends up with the result of everyone saying "well we know what you mean" or "we know what your trying to say". So how are we supposed to figure this out? Does it not matter because the meaning still gets across? Or does the choice of how you say it change based on the context? Are both past tense or is just one of the words turn into past tense form? I personally have no clue whats so ever and forgot how annoyed I am about not knowing this until after class. 

Lets take a look at these two sentences: 
"I blow dried my hair."
"I blew dried my hair."

Both sound as though they could work, but blow dried sounds better. But then lets take a look at these two options:
"I blowed dry my hair."
"I blew dry my hair."

I think both of those sound correct as well and you know it was in the past and that the action was blowing your hair dry. So looking at these sentences what can you deduct? Is it the action of blowing that needs to be changed into past tense or is the drying that needs to be past tense? I personally think that if you choose to keep blow as blow then it should be dry that changes to dried, but if you choose to change blow to blew then dry should stay as dry. 

I am only trying to understand how to phrase this with just the words blow and dry because there are other ways of saying this such as "I've blown dry my hair" but I may very well be confusing myself even more on the matter or confusing those who were once confident on how to say this statement and for that I apologize. Thoughts are more than welcome on the subject!