What are the solutions to the equation 2x^2=6x-6 ?

The solutions to the equation 2x^2=6x-6 are x= 3/2+i(sqrt(3))/2 ,x= 3/2-i(sqrt(3))/2

Find the zeros of 2x^2=6x-6

The zeros of 2x^2=6x-6 are x= 3/2+i(sqrt(3))/2 ,x= 3/2-i(sqrt(3))/2

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2 x^{2} = 6 x - 6

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

Solution steps

2 x^{2} = 6 x - 6

Move

6

to the left side

2 x^{2} + 6 = 6 x

Move

6 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 2 \cdot 6}{2 \cdot 2}

Simplify

(- 6)^{2} - 4 \cdot 2 \cdot 6 : 23 i

x_{1, 2} = \frac{- ( - 6 ) \pm 2 3 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 3 i}{2 \cdot 2}, x_{2} = \frac{- ( - 6 ) - 2 3 i}{2 \cdot 2}

x = \frac{- ( - 6 ) + 2 3 i}{2 \cdot 2} : \frac{3}{2} + i \frac{3}{2}

x = \frac{- ( - 6 ) - 2 3 i}{2 \cdot 2} : \frac{3}{2} - i \frac{3}{2}

The solutions to the quadratic equation are:

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

12 x^{2} - 72 x - 84 = 0

n^{2} - 159 = 10

x^{2} + 18 = - 6 x

- 4 x^{2} = - 8

x^{2} + 2 x^{2} = 16

What are the solutions to the equation 2x^2=6x-6 ?
The solutions to the equation 2x^2=6x-6 are x= 3/2+i(sqrt(3))/2 ,x= 3/2-i(sqrt(3))/2
Find the zeros of 2x^2=6x-6
The zeros of 2x^2=6x-6 are x= 3/2+i(sqrt(3))/2 ,x= 3/2-i(sqrt(3))/2