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

Step-by-step Solution

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Final Answer

$x=-0.5+0.866025i,\:x=-0.5-0.866025i$
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Step-by-step Solution

Problem to solve:

$x^2+x+1=0$

Specify 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.

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

Unlock the first 3 steps of this solution!

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.

Final Answer

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

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Got another answer? Verify it!

Go!
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

Tips on how to improve your answer:

$x^2+x+1=0$

Main topic:

Quadratic equations

Related Formulas:

1. See formulas

Time to solve it:

~ 0.05 s