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

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

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

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

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x^{3} + x = - 2

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

Solution steps

x^{3} + x = - 2

Move

2

to the left side

x^{3} + x + 2 = 0

Factor

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

x^{3} + x = 10

x^{5} - 3 x^{3} - 4 x^{2} + 2 x + 4 = 0

n^{3} = 60

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

x^{3} - 8 x = 0

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