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4x squared - x cubed = 506

x squared times (4 - x) = 506

prime factors of 506 are 2, 11 & 23 so possible factors are 22 x 23 and 11 x 46.

None of these are square numbers so first impression is that there is no solution in integers. I also suspect that any solution will be negative.

More later!

Later: Nearest I can get without going to ten-thousandths is x = -6.834.

4xsquared = 186.814, x cubed = -319.172 which sum to 505.986.

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