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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