What are the solutions to the equation x^3=x^5+x^3+x ?

The solutions to the equation x^3=x^5+x^3+x are

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x^3=x^5+x^3+x

x^{3} = x^{5} + x^{3} + x

x = 0, x = - \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2}{2} - i \frac{2}{2}

Solution steps

x^{3} = x^{5} + x^{3} + x

Switch sides

x^{5} + x^{3} + x = x^{3}

Move

x^{3}

to the left side

x^{5} + x = 0

Factor

x^{5} + x : x (x^{2} + 2 x + 1) (x^{2} - 2 x + 1)

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

Solve

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

Solve

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

The solutions are

x = 0, x = - \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2}{2} - i \frac{2}{2}

x^{4} - 5 x^{3} - 15 x^{2} + 5 x + 14 = 0

x, x^{3} - 3 y^{2} + 3 y - 1 = 0

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

- x^{3} - 6 x^{2} + 6 x + 28 = 0

x^{5} - 6 x^{4} + 11 x^{3} - 6 x^{2} = 0

What are the solutions to the equation x^3=x^5+x^3+x ?
The solutions to the equation x^3=x^5+x^3+x are
Find the zeros of x^3=x^5+x^3+x
The zeros of x^3=x^5+x^3+x are