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

The solutions to the equation x=-x^3 are x=0,x=i,x=-i

Find the zeros of x=-x^3

The zeros of x=-x^3 are x=0,x=i,x=-i

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x = - x^{3}

x = 0, x = i, x = - i

Solution steps

x = - x^{3}

Switch sides

- x^{3} = x

Move

x

to the left side

- x^{3} - x = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

x = 0, x = i, x = - i

0 = x^{3} - 7 x^{2} - x + 7

x^{3} + 2 x^{2} - 40 x + 64 = 0

x^{3} + 3 x^{2} - 4 x - 12 = 0

z^{4} = - 83 + 8 i

2 = \frac{4}{3} π r^{3}

What are the solutions to the equation x=-x^3 ?
The solutions to the equation x=-x^3 are x=0,x=i,x=-i
Find the zeros of x=-x^3
The zeros of x=-x^3 are x=0,x=i,x=-i