Not many solutions? Part 2

Algebra Level 3

Let the functions f(x)f(x) and g(x)g(x) be f(x)=x32x2+x2f(x)=x^{3}-2x^{2}+x-2 and g(x)=x2+1g(x)=x^{2}+1 .

Find the sum of all real solutions to the equation

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


Part 1.

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