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Step-by-step Solution

Solve the equation $x^2+x+1=0$

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Answer

$x_1=-0.5+0.866i,\:x_2=-0.5-0.866i$

Step-by-step explanation

Problem to solve:

$x^2+x+1=0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=1$ and $c=1$

$x =\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
2

Substituting the values of the coefficients of the equation in the quadratic formula

$x=\frac{-1\pm \sqrt{-3}}{2}$

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Answer

$x_1=-0.5+0.866i,\:x_2=-0.5-0.866i$
$x^2+x+1=0$

Main topic:

Equations

Time to solve it:

~ 0.43 seconds