What are the solutions to the equation x^3-18x+27=0 ?

The solutions to the equation x^3-18x+27=0 are x=3,x=(-3+3sqrt(5))/2 ,x=(-3-3sqrt(5))/2

Find the zeros of x^3-18x+27=0

The zeros of x^3-18x+27=0 are x=3,x=(-3+3sqrt(5))/2 ,x=(-3-3sqrt(5))/2

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x^{3} - 18 x + 27 = 0

x = 3, x = \frac{- 3 + 3 5}{2}, x = \frac{- 3 - 3 5}{2}

Decimal Notation

x = 3, x = 1.85410 \dots, x = - 4.85410 \dots

Solution steps

x^{3} - 18 x + 27 = 0

Factor

x^{3} - 18 x + 27 : (x - 3) (x^{2} + 3 x - 9)

(x - 3) (x^{2} + 3 x - 9) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} + 3 x - 9 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 3 x - 9 = 0 : x = \frac{- 3 + 3 5}{2}, x = \frac{- 3 - 3 5}{2}

The solutions are

x = 3, x = \frac{- 3 + 3 5}{2}, x = \frac{- 3 - 3 5}{2}

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

y^{3} - 3 y - 52 = 0

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

x^{3} = 1000

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

What are the solutions to the equation x^3-18x+27=0 ?
The solutions to the equation x^3-18x+27=0 are x=3,x=(-3+3sqrt(5))/2 ,x=(-3-3sqrt(5))/2
Find the zeros of x^3-18x+27=0
The zeros of x^3-18x+27=0 are x=3,x=(-3+3sqrt(5))/2 ,x=(-3-3sqrt(5))/2