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

The solutions to the equation x^3=2x-x^2 are x=0,x=1,x=-2

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

The zeros of x^3=2x-x^2 are x=0,x=1,x=-2

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

x = 0, x = 1, x = - 2

Solution steps

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

Move

x^{2}

to the left side

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

Move

2 x

to the left side

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

Factor

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

x (x - 1) (x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x + 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 2 = 0 : x = - 2

The solutions are

x = 0, x = 1, x = - 2

u^{3} = 8000

\frac{1}{3} x^{3} - 2 x = 0

x^{3} + 5 x - 26 = 0

(x + 1)^{3} = - 8

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

What are the solutions to the equation x^3=2x-x^2 ?
The solutions to the equation x^3=2x-x^2 are x=0,x=1,x=-2
Find the zeros of x^3=2x-x^2
The zeros of x^3=2x-x^2 are x=0,x=1,x=-2