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Step-by-step Solution

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

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$x=-0.5+0.866025i,\:x=-0.5-0.866025i$

Step-by-step Solution

Problem to solve:

$x^2+x+1=0$

Choose the solving method

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:

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

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

Learn how to solve quadratic equations problems step by step online.

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

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation x^2+x+1=0. 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:<ul><li>\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</li></ul>. To obtain the two solutions, divide the equation in two equations, one when \pm is positive (+), and another when \pm is negative (-). Calculate the power \sqrt{-3} using complex numbers. Calculate the power \sqrt{-3} using complex numbers.

$x=-0.5+0.866025i,\:x=-0.5-0.866025i$
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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$x^2+x+1=0$