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

The solutions to the equation x^3=2-x are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

Find the zeros of x^3=2-x

The zeros of x^3=2-x are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2

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x^{3} = 2 - x

x = 1, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

Solution steps

x^{3} = 2 - x

Move

x

to the left side

x^{3} + x = 2

Move

2

to the left side

x^{3} + x - 2 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + x + 2 = 0 : x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

The solutions are

x = 1, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

x^{3} - 4 x^{2} + 16 x - 64 = 0

x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1 = 0

4 x^{3} + 8 x^{2} - 32 x = 0

3 y = 4 y^{3}

30 π r^{2} + 4 π r^{3} - 4500 = 0

What are the solutions to the equation x^3=2-x ?
The solutions to the equation x^3=2-x are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2
Find the zeros of x^3=2-x
The zeros of x^3=2-x are x=1,x=-1/2+i(sqrt(7))/2 ,x=-1/2-i(sqrt(7))/2