I am solving the following problem: Find all real x such that ##x^3 + 3x^2 + 3x = 1##(adsbygoogle = window.adsbygoogle || []).push({});

I complete the cube by adding 1 to both sides, and get that ##(x + 1)^3 = 2## then ##x = 2^{1/3} - 1##

What I'm asking is how can I be sure that I have found all real solutions? What if there are other solutions?

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# B Showing all solutions to a cubic equation

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