x^2=-27/x

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Solution for x^2=-27/x equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

x^2 = -27/x // + -27/x

x^2-(-27/x) = 0

x^2+27*x^-1 = 0

1*x^2+27*x^-1 = 0

(1*x^3+27*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^3+27*x^0) = 0

x^1

x^3+27 = 0

{ 1, -1, 3, -3, 9, -9, 27, -27 }

1

x = 1

x^3+27 = 28

1

-1

x = -1

x^3+27 = 26

-1

3

x = 3

x^3+27 = 54

3

-3

x = -3

x^3+27 = 0

-3

x+3

x^2-3*x+9

x^3+27

x+3

-x^3-3*x^2

27-3*x^2

3*x^2+9*x

9*x+27

-9*x-27

0

x^2-3*x+9 = 0

DELTA = (-3)^2-(1*4*9)

DELTA = -27

DELTA < 0

x in { -3} 

x = -3

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