What are the solutions to the equation x^3=-9x ?

The solutions to the equation x^3=-9x are x=0,x=3i,x=-3i

Find the zeros of x^3=-9x

The zeros of x^3=-9x are x=0,x=3i,x=-3i

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x^{3} = - 9 x

x = 0, x = 3 i, x = - 3 i

Solution steps

x^{3} = - 9 x

Move

9 x

to the left side

x^{3} + 9 x = 0

Factor

x^{3} + 9 x : x (x^{2} + 9)

x (x^{2} + 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} + 9 = 0

Solve

x^{2} + 9 = 0 : x = 3 i, x = - 3 i

The solutions are

x = 0, x = 3 i, x = - 3 i

(1 + x)^{10} = 2

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

15 x^{3} + 14 x^{2} - 8 x = 90

x^{3} + 9 x^{2} + 26 x + 24 = 0

x^{4} = i

What are the solutions to the equation x^3=-9x ?
The solutions to the equation x^3=-9x are x=0,x=3i,x=-3i
Find the zeros of x^3=-9x
The zeros of x^3=-9x are x=0,x=3i,x=-3i