Bad luck with thermostat replacement

Hello Everyone
We tried to replace the thermostat in our 1995 Escort LX Wagon. Unfortunately the head of one of the bolts (top) holding the thermostat
housing to the cylinder head broke off. We tried to drill it out but the drill broke too. Now we cannot do a thing other than take the car to a garage to get fixed. Does anyone has an idea how can they fix this and how much will it cost?
Thanks a lot for your reply.
Erica
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Most people will use an easy-out. You drill a smaller hole in the bolt, and the easy-out goes in that hole. An easy-out is kind of like a reverse drill bit. It grips whats left of the bolt after it has been drilled out. They could possibly go through a couple of bits removing it.
If that does not work, they will drill out the whole thing including the threads, tap new threads in for an oversize bolt, open up the hole of the t-stat housing and put a larger bolt in.
C. Vaughan

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Does the cylinder head has to be removed from the car for the drilling?
Thank you.
Erica

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