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

The solutions to the equation x=x^3-x are x=0,x=-sqrt(2),x=sqrt(2)

Find the zeros of x=x^3-x

The zeros of x=x^3-x are x=0,x=-sqrt(2),x=sqrt(2)

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x = x^{3} - x

x = 0, x = - 2, x = 2

Solution steps

x = x^{3} - x

Switch sides

x^{3} - x = x

Move

x

to the left side

x^{3} - 2 x = 0

Factor

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

x (x + 2) (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 2 = 0 or x - 2 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

The solutions are

x = 0, x = - 2, x = 2

2 x^{3} - 128 = 0

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

9 x^{3} + x^{2} - 81 x - 9 = 0

x = x^{3} + 1

12 x^{3} = - 3 x^{2} - 12

What are the solutions to the equation x=x^3-x ?
The solutions to the equation x=x^3-x are x=0,x=-sqrt(2),x=sqrt(2)
Find the zeros of x=x^3-x
The zeros of x=x^3-x are x=0,x=-sqrt(2),x=sqrt(2)