7k to spend on an 8k trade-in car doesn't make financial sense. You need to either find someone who can do an engine replacement cheaper for you, or if this proves to be a serious engine problem and you can't do it any cheaper, just sell the car locally to someone who has the mechanical know-how to do the job themselves. They should be willing to pay you more than 1k for it.

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Currently driving: 2011 E70 x35i , 2011 E90 335d
Previous BMWs: 2007 E90 328i , 2005 E53 3.0i, 2011 F10 535i (6spd manual)