What are the solutions to the equation x^3=10-x ?

The solutions to the equation x^3=10-x are x=2,x=-1+2i,x=-1-2i

Find the zeros of x^3=10-x

The zeros of x^3=10-x are x=2,x=-1+2i,x=-1-2i

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x^{3} = 10 - x

x = 2, x = - 1 + 2 i, x = - 1 - 2 i

Solution steps

x^{3} = 10 - x

Move

x

to the left side

x^{3} + x = 10

Move

10

to the left side

x^{3} + x - 10 = 0

Factor

x^{3} + x - 10 : (x - 2) (x^{2} + 2 x + 5)

(x - 2) (x^{2} + 2 x + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} + 2 x + 5 = 0

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

x = 2, x = - 1 + 2 i, x = - 1 - 2 i

x, x^{4} + x^{2} y^{2} + y^{3} = 5

6 x^{5} - 12 x^{3} - 3 = 0

5 x^{3} + 8 x^{2} - 9 x + 2 = 0

x^{3} + 5 x^{2} + 3 x + 15 = 0

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

What are the solutions to the equation x^3=10-x ?
The solutions to the equation x^3=10-x are x=2,x=-1+2i,x=-1-2i
Find the zeros of x^3=10-x
The zeros of x^3=10-x are x=2,x=-1+2i,x=-1-2i