x=8
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x2-5x = 24 x2-5x-24 = 0 (x-8)(x+3) = 0 x = 8 or x -3
x2 + 5x - 594 = 0 You need two factors of 594 whose difference by 5. They are 22 and 27. So x = 22 or x = -27
It is, as stated, x2 - 5x + 25/4 = 0
Suppose the number is x. Then x2 = 5x + 24 or x2 - 5x - 24 = 0 Then x2 - 8x + 3x - 24 = 0 or x(x - 8) + 3(x - 8) = 0 that is (x - 8)*(x + 3) = 0 so that x = 8 or x = -3 Since the number is a natural number, it cannot be -3, and so the answer is 8.
The discriminant is 9.