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Calculus Level 3

If $$f(x) = x^2 + x g'(1) + g''(2)$$ and $$g(x) = f(1)x^2 + xf'(x) + f''(x) ~\forall ~x\in \mathbb{R}$$, and if $$f(x)$$ is in the form of $$ax^2 + bx$$ and $$g'(x) = -c$$, find the value of $$a + 2b + 3c$$.

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