What are the solutions to the equation 0=x^2-x+1 ?

The solutions to the equation 0=x^2-x+1 are x= 1/2+i(sqrt(3))/2 ,x= 1/2-i(sqrt(3))/2

Find the zeros of 0=x^2-x+1

The zeros of 0=x^2-x+1 are x= 1/2+i(sqrt(3))/2 ,x= 1/2-i(sqrt(3))/2

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0 = x^{2} - x + 1

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

Solution steps

0 = x^{2} - x + 1

Switch sides

x^{2} - x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

Simplify

(- 1)^{2} - 4 \cdot 1 \cdot 1 : 3 i

x_{1, 2} = \frac{- ( - 1 ) \pm 3 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 3 i}{2 \cdot 1}, x_{2} = \frac{- ( - 1 ) - 3 i}{2 \cdot 1}

x = \frac{- ( - 1 ) + 3 i}{2 \cdot 1} : \frac{1}{2} + i \frac{3}{2}

x = \frac{- ( - 1 ) - 3 i}{2 \cdot 1} : \frac{1}{2} - i \frac{3}{2}

The solutions to the quadratic equation are:

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

7500000 = - 0.5 x^{2} + 2000 x + 6000000

3 a^{2} - 10 a + 2 = 0

3 x^{2} + 30 x + 75 = 0

x^{2} - 9 x = - 14

x^{2} + 5 x - 20 = 4

What are the solutions to the equation 0=x^2-x+1 ?
The solutions to the equation 0=x^2-x+1 are x= 1/2+i(sqrt(3))/2 ,x= 1/2-i(sqrt(3))/2
Find the zeros of 0=x^2-x+1
The zeros of 0=x^2-x+1 are x= 1/2+i(sqrt(3))/2 ,x= 1/2-i(sqrt(3))/2