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

## Step-by-step Solution

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###  Videos

$x=\frac{-1+\sqrt{3}i}{2},\:x=\frac{-1-\sqrt{3}i}{2}$
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##  Step-by-step Solution 

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1

Move everything to the left hand side of the equation

$0-x^2-x-1=0$

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

$0-x^2-x-1=0$

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation 0=x^2+x+1. Move everything to the left hand side of the equation. Subtract the values 0 and -1. For a simpler handling of the equation, change the sign of all terms, multiplying the entire whole by -1. Multiply -1 times -1.

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

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve for xFind the rootsSolve by factoringSolve by completing the squareSolve by quadratic formulaFind break even pointsFind the discriminant

SnapXam A2

### beta Got a different 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

The quadratic equations (or second degree equations) are those equations where the greatest exponent to which the unknown is raised is the exponent 2.

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