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

The solutions to the equation x^2+2=x are x= 1/2+i(sqrt(7))/2 ,x= 1/2-i(sqrt(7))/2

Find the zeros of x^2+2=x

The zeros of x^2+2=x are x= 1/2+i(sqrt(7))/2 ,x= 1/2-i(sqrt(7))/2

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x^{2} + 2 = x

x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

Solution steps

x^{2} + 2 = x

Move

x

to the left side

x^{2} + 2 - x = 0

Write in the standard form

a x^{2} + b x + c = 0

x^{2} - x + 2 = 0

Solve with the quadratic formula

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

Simplify

(- 1)^{2} - 4 \cdot 1 \cdot 2 : 7 i

x_{1, 2} = \frac{- ( - 1 ) \pm 7 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 7 i}{2 \cdot 1}, x_{2} = \frac{- ( - 1 ) - 7 i}{2 \cdot 1}

x = \frac{- ( - 1 ) + 7 i}{2 \cdot 1} : \frac{1}{2} + i \frac{7}{2}

x = \frac{- ( - 1 ) - 7 i}{2 \cdot 1} : \frac{1}{2} - i \frac{7}{2}

The solutions to the quadratic equation are:

x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

\frac{1}{4} x^{2} - 12 = - 3

x^{2} + 12 x + 36 = 49

x^{2} - 45 x - 4

3 x^{2} + 14 x - 6 = 0

3 x^{2} + 4 = 52

What are the solutions to the equation x^2+2=x ?
The solutions to the equation x^2+2=x are x= 1/2+i(sqrt(7))/2 ,x= 1/2-i(sqrt(7))/2
Find the zeros of x^2+2=x
The zeros of x^2+2=x are x= 1/2+i(sqrt(7))/2 ,x= 1/2-i(sqrt(7))/2