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$\large f_n(x)=x^2 + ( x + 1) ^2 +(x+2)^2+\ldots+(x+n)^2$

The function $f_n(x)$ is defined above for $x$ ranges over all real values with natural number $n$.

If the minimum value of $f_n(x)$ is $(2^{10}-12)$ then find the value of $n$.

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