Negotiating Prices

I am having some work done on a 1000 sq ft apt (painting, shining floors, total reno of kitchen and bathroom, and smaller things throughout). I have been given two estimates of $35K and $38K. My question is, is it customary to negotiate a price down with contractors? And if so, can you give me some pointers and suggestions as to how to go about this without offending them? (Obviously I have never done this before.) Thanks in advance.

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