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Are you attempting to solve for x using the complete the square method?

I'm trying to get the sum of 2 solutions of the equation \[X^{2}+5x-24=0\]

you mean the product of two solutions, in other words you want to factorise the quadratic

(x+a)(x+b) = x^2 +5x -24

Hmm. I don't get -5 as one of the solutions?