What are the solutions to the equation x^3-27x=-10 ?

The solutions to the equation x^3-27x=-10 are x=5,x=(-5+sqrt(33))/2 ,x=(-5-sqrt(33))/2

Find the zeros of x^3-27x=-10

The zeros of x^3-27x=-10 are x=5,x=(-5+sqrt(33))/2 ,x=(-5-sqrt(33))/2

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x^{3} - 27 x = - 10

x = 5, x = \frac{- 5 + 33}{2}, x = \frac{- 5 - 33}{2}

Solution steps

x^{3} - 27 x = - 10

Move

10

to the left side

x^{3} - 27 x + 10 = 0

Factor

x^{3} - 27 x + 10 : (x - 5) (x^{2} + 5 x - 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 5 = 0 : x = 5

Solve

x^{2} + 5 x - 2 = 0 : x = \frac{- 5 + 33}{2}, x = \frac{- 5 - 33}{2}

The solutions are

x = 5, x = \frac{- 5 + 33}{2}, x = \frac{- 5 - 33}{2}

x^{3} - 13 x^{2} + 56 x - 80 = 0

(t)^{3} = 1.55

9 m^{5} = 27 m^{3}

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

16 x^{4} - 25 x^{2} = 0

What are the solutions to the equation x^3-27x=-10 ?
The solutions to the equation x^3-27x=-10 are x=5,x=(-5+sqrt(33))/2 ,x=(-5-sqrt(33))/2
Find the zeros of x^3-27x=-10
The zeros of x^3-27x=-10 are x=5,x=(-5+sqrt(33))/2 ,x=(-5-sqrt(33))/2