What is wrong with the proof?

Algebra Level 3
1. Let $x$ be a solution of $x^{2} + x + 1 = 0$
2. Since $x$ is not 0, we can divide both sides by $x$:
• $x + 1 + \frac{1}{x} = 0$
3. Substitute $x + 1 = -x^{2}$
• $\frac{1}{x} = x^{2}$
4. $x = 1$
• $x = x^{3}$
5. $3 = 0$
• $1^{2} + 1 + 1 = 0$
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