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

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

Find the zeros of x=x(x-2)^2

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

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

x = 0, x = 1, x = 3

Solution steps

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

Expand

x (x - 2)^{2} : x^{3} - 4 x^{2} + 4 x

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

Switch sides

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

Move

x

to the left side

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

Factor

x^{3} - 4 x^{2} + 3 x : x (x - 1) (x - 3)

x (x - 1) (x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x - 3 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 3 = 0 : x = 3

The solutions are

x = 0, x = 1, x = 3

2 x^{3} - x^{2} - 15 x + 18 = 0

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

x^{3} - 2 x^{2} + 5 x - 6 = 0

4 = x^{10}

0 = x^{4} - 7 x^{2} + 12

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