# Step-by-step Solution

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

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### Videos

$x=\frac{-1+\sqrt{-3}}{2},\:x=\frac{-1-1\cdot \sqrt{-3}}{2}$

## 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 in this case $a=1$, $b=1$ and $c=1$. Then substitute the values of the coefficients of the equation in the quadratic formula:

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

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

To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)

$x=\frac{-1+\sqrt{-3}}{2},\:x=\frac{-1-1\cdot \sqrt{-3}}{2}$

$x=\frac{-1+\sqrt{-3}}{2},\:x=\frac{-1-1\cdot \sqrt{-3}}{2}$
$x^2+x+1=0$