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

The solutions to the equation x^3-2x^2=x are x=0,x=1+sqrt(2),x=1-sqrt(2)

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

The zeros of x^3-2x^2=x are x=0,x=1+sqrt(2),x=1-sqrt(2)

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

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

Decimal Notation

x = 0, x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

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

Move

x

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

The solutions are

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

6527 3^{2} = w^{4} + 4 w^{2}

12 x^{3} - 24 x^{2} + 12 x = 0

(z^{2} + 7)^{2} = 0

15 x^{3} + 6 x^{2} - 10 x - 4 = 0

x^{3} - 11 x + 150 = 0

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