How many solutions are there to $(x^2+1)^{10} = 2x - x^2 - 2$?

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The equation \[(x^2+1)^{10} = 2x - x^2 - 2\]

1. has \(x=2\) as a solution;

2. has no real solutions;

3. has an odd number of real solutions;

4. has twenty real solutions.

Could we draw the graphs of the functions on the left and right hand sides of the equation?

Can we write the quadratic on the right hand side in a different (more useful) form?