Not many solutions? Part 2

Algebra Level 3

Let the functions \(f(x)\) and \(g(x)\) be \(f(x)=x^{3}-2x^{2}+x-2\) and \(g(x)=x^{2}+1\) .

Find the sum of all real solutions to the equation

\(f(x)+g(x)=0\).


Part 1.

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