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You are entitled to the "benefit of the bargain" - meaning the contractor must perform the contract as agreed to, and for the price agreed to.
If you cannot reach an agreement, you can sue the contractor for breach of contract (you can sue for either (a) cost of repair - cost of having another contractor come and perform the job properly, including materials; or (b) "specific performance" (requiring the contractor to come back and do the job properly).
Short of filing a lawsuit, you can try to mediate the dispute with them - contact your local bar association and request referrals to mediators, a third party neutral can often help you reach a mutually agreeable resolution. Use the bar association's referrals to contact a mediator or two, the mediator will then contact the other party to set up a mediation session, and you can go from there - hopefully resulting in a formal or written settlement agreement, and save yourself the time and expense of litigation.