$$ x^{2}+x+1=0 $$ - $$ x_{1}=0 $$ $$ \cdot x_{2}=-1 $$

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The correct solutions to the equation $$ x^2 + x + 1 = 0 $$ are complex numbers: $$ x_1 = \frac{-1 + i\sqrt{3}}{2} $$ and $$ x_2 = \frac{-1 - i\sqrt{3}}{2} $$. The equation you provided is $$ x^2 + x + 1 = 0 $$. To solve this quadratic equation, we can use the quadratic formula: $$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$ In this case, $$ a = 1 $$, $$ b = 1 $$, and $$ c = 1 $$. Plugging these values into the formula gives: $$ x = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot 1}}{2 \cdot 1} $$ $$ x = \frac{-1 \pm \sqrt{1 - 4}}{2} $$ $$ x = \frac{-1 \pm \sqrt{-3}}{2} $$ $$ x = \frac{-1 \pm i\sqrt{3}}{2} $$ Thus, the solutions to the equation $$ x^2 + x + 1 = 0 $$ are: $$ x_1 = \frac{-1 + i\sqrt{3}}{2}, \quad x_2 = \frac{-1 - i\sqrt{3}}{2} $$ These solutions are complex numbers, not real numbers. Therefore, the values $$ x_1 = 0 $$ and $$ x_2 = -1 $$ you provided are incorrect. The correct solutions are the complex numbers shown above.

\( x^{2}+x+1=0 \) - \( x_{1}=0 \) \( \cdot x_{2}=-1 \)

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\( x^{2}+x+1=0 \) - \( x_{1}=0 \) \( \cdot x_{2}=-1 \)

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