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As an equation, x/x = x2, or x2 = x/x. Multiplying both sides by x: x3 = x. Put everything on the left side: x3 - x = 0. Factoring the left part: x(x2 - 1) = 0, or x(x+1)(x-1) = 0. This has the solutions 0, 1, -1. However, 0 doesn't make sense in the original equation - it seems that multiplying with "x" introduced an extra solution.

The remaining solutions, 1 and -1, fit the original specification.

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Q: Can any number divided by itself equal to the square of the original number?
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