SOLUTION: find all positive values for k for which each of the following can be factored. x^2+x-k

k must be the product of two integers that differ by 1

Let one integer be n and and the other n+1.

Then the product of n and n+1 is n(n + 1)

So k must be such that k = n(n + 1) where n is any integer.
That's it. 

Edwin