# Carelessly Cake

John Cake is a very indeed seriously careless person.

One day, he came up with five numbers: $x^2+1$ $x^2-1$ $2x$ $x^2+2x$ $3x-5$

($$x$$ is an integer)

He chose 4 of them, and wanted to take the sum of the 4 numbers chosen, but instead, he carelessly added one of the chosen 4 numbers twice, getting 47 as the wrong sum.

If the correct sum is $$S$$, what is the sum of all possible values of $$S$$?

This is one part of 1+1 is not = to 3.

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