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

The solutions to the equation 2x^2-3x=x-x^3 are x=0,x=-1+sqrt(5),x=-1-sqrt(5)

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

The zeros of 2x^2-3x=x-x^3 are x=0,x=-1+sqrt(5),x=-1-sqrt(5)

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

x = 0, x = - 1 + 5, x = - 1 - 5

Solution steps

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

Switch sides

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

Move

3 x

to the left side

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

Move

2 x^{2}

to the left side

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

Factor

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

- x (x^{2} + 2 x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{2} + 2 x - 4 = 0 : x = - 1 + 5, x = - 1 - 5

The solutions are

x = 0, x = - 1 + 5, x = - 1 - 5

x, x^{4} + y^{4} + 2 = 0

- x^{4} + 8 x^{3} - 18 x^{2} = 0

- x^{3} + 10 x^{2} - 29 x + 20 = 0

69 = c^{3}

x^{4} + 8 x^{3} + 9 x^{2} - 28 x + 10 = 0

What are the solutions to the equation 2x^2-3x=x-x^3 ?
The solutions to the equation 2x^2-3x=x-x^3 are x=0,x=-1+sqrt(5),x=-1-sqrt(5)
Find the zeros of 2x^2-3x=x-x^3
The zeros of 2x^2-3x=x-x^3 are x=0,x=-1+sqrt(5),x=-1-sqrt(5)