What are the solutions to the equation -2x^3-2x+14=10 ?

The solutions to the equation -2x^3-2x+14=10 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

Find the zeros of -2x^3-2x+14=10

The zeros of -2x^3-2x+14=10 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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- 2 x^{3} - 2 x + 14 = 10

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

Solution steps

- 2 x^{3} - 2 x + 14 = 10

Move

10

to the left side

- 2 x^{3} - 2 x + 4 = 0

Factor

- 2 x^{3} - 2 x + 4 : - 2 (x - 1) (x^{2} + x + 2)

- 2 (x - 1) (x^{2} + x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + x + 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x + 2 = 0 : x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

The solutions are

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

2 x^{4} = 24 x^{2}

6 x^{4} + 13 x^{3} - 8 x^{2} - 17 x + 6 = 0

4 x^{4} + 2 x^{2} - 1 = 0

y, y^{2} = x^{2} - x^{4}

2 x^{5} - 2 x^{3} = 0

What are the solutions to the equation -2x^3-2x+14=10 ?
The solutions to the equation -2x^3-2x+14=10 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2
Find the zeros of -2x^3-2x+14=10
The zeros of -2x^3-2x+14=10 are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2