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

## Step-by-step Solution

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asin
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sinh
cosh
tanh
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asinh
acosh
atanh
acoth
asech
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### Videos

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

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

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

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

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

Calculate the power $\sqrt{-3}$ using complex numbers

$x=\frac{1+1.732051i}{2},\:x=\frac{1-\sqrt{-3}}{2}$
4

Calculate the power $\sqrt{-3}$ using complex numbers

$x=\frac{1+1.732051i}{2},\:x=\frac{1-1.732051i}{2}$
5

Expand the fraction $\frac{1+1.732051i}{2}$ into $2$ simpler fractions with common denominator $2$

$x=\frac{1}{2}+\frac{1.732051i}{2},\:x=\frac{1-1.732051i}{2}$

Take $\frac{\sqrt{3}}{2}$ out of the fraction

$x=0.5+0.866025i,\:x=\frac{1-1.732051i}{2}$
6

Simplify

$x=0.5+0.866025i,\:x=\frac{1-1.732051i}{2}$
7

Expand the fraction $\frac{1-1.732051i}{2}$ into $2$ simpler fractions with common denominator $2$

$x=0.5+0.866025i,\:x=\frac{1}{2}+\frac{-1.732051i}{2}$

Take $\frac{-\sqrt{3}}{2}$ out of the fraction

$x=0.5+0.866025i,\:x=0.5-0.866025i$
8

Simplify

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

$x=0.5+0.866025i,\:x=0.5-0.866025i$
SnapXam A2

### beta 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

$x^2-x+1=0$