(7x+2)/(7x^3-40x^2-40x-8)

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Solution for (7x+2)/(7x^3-40x^2-40x-8) equation: 


D( x )

7*x^3-(40*x^2)-(40*x)-8 = 0

7*x^3-(40*x^2)-(40*x)-8 = 0

7*x^3-(40*x^2)-(40*x)-8 = 0

7*x^3-40*x^2-40*x-8 = 0

7*x^3-40*x^2-40*x-8 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8 }

1

x = 1

7*x^3-40*x^2-40*x-8 = -81

1

-1

x = -1

7*x^3-40*x^2-40*x-8 = -15

-1

2

x = 2

7*x^3-40*x^2-40*x-8 = -192

2

-2

x = -2

7*x^3-40*x^2-40*x-8 = -144

-2

4

x = 4

7*x^3-40*x^2-40*x-8 = -360

4

-4

x = -4

7*x^3-40*x^2-40*x-8 = -936

-4

8

x = 8

7*x^3-40*x^2-40*x-8 = 696

8

-8

x = -8

7*x^3-40*x^2-40*x-8 = -5832

-8

{ 1/7, -1/7, -1/7, 1/7, 2/7, -2/7, -2/7, 2/7, 4/7, -4/7, -4/7, 4/7, 8/7, -8/7, -8/7, 8/7 }

1/7

x

1/7

7*x^3-40*x^2-40*x-8 = -14.51020408

1/7

-1/7

x

-1/7

7*x^3-40*x^2-40*x-8 = -3.12244898

-1/7

-1/7

x

-1/7

7*x^3-40*x^2-40*x-8 = -3.12244898

-1/7

1/7

x

1/7

7*x^3-40*x^2-40*x-8 = -14.51020408

1/7

2/7

x

2/7

7*x^3-40*x^2-40*x-8 = -22.53061224

2/7

-2/7

x

-2/7

7*x^3-40*x^2-40*x-8 = 0

-2/7

x+2/7

7*x^2-42*x-28

7*x^3-40*x^2-40*x-8

x+2/7

-7*x^3-2*x^2

-42*x^2-40*x-8

42*x^2+12*x

-28*x-8

28*x+8

0

7*x^2-42*x-28 = 0

DELTA = (-42)^2-(-28*4*7)

DELTA = 2548

DELTA > 0

x = (2548^(1/2)+42)/(2*7) or x = (42-2548^(1/2))/(2*7)

x = (14*13^(1/2)+42)/14 or x = (42-14*13^(1/2))/14

x in { (42-14*13^(1/2))/14, (14*13^(1/2)+42)/14, -2/7} 

x in (-oo:(42-14*13^(1/2))/14) U ((42-14*13^(1/2))/14:-2/7) U (-2/7:(14*13^(1/2)+42)/14) U ((14*13^(1/2)+42)/14:+oo)

(7*x+2)/(7*x^3-(40*x^2)-(40*x)-8) = 0

(7*x+2)/(7*x^3-40*x^2-40*x-8) = 0

7*x^3-40*x^2-40*x-8 = 0

7*x^3-40*x^2-40*x-8 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8 }

1

x = 1

7*x^3-40*x^2-40*x-8 = -81

1

-1

x = -1

7*x^3-40*x^2-40*x-8 = -15

-1

2

x = 2

7*x^3-40*x^2-40*x-8 = -192

2

-2

x = -2

7*x^3-40*x^2-40*x-8 = -144

-2

4

x = 4

7*x^3-40*x^2-40*x-8 = -360

4

-4

x = -4

7*x^3-40*x^2-40*x-8 = -936

-4

8

x = 8

7*x^3-40*x^2-40*x-8 = 696

8

-8

x = -8

7*x^3-40*x^2-40*x-8 = -5832

-8

{ 1/7, -1/7, -1/7, 1/7, 2/7, -2/7, -2/7, 2/7, 4/7, -4/7, -4/7, 4/7, 8/7, -8/7, -8/7, 8/7 }

1/7

x

1/7

7*x^3-40*x^2-40*x-8 = -14.51020408

1/7

-1/7

x

-1/7

7*x^3-40*x^2-40*x-8 = -3.12244898

-1/7

-1/7

x

-1/7

7*x^3-40*x^2-40*x-8 = -3.12244898

-1/7

1/7

x

1/7

7*x^3-40*x^2-40*x-8 = -14.51020408

1/7

2/7

x

2/7

7*x^3-40*x^2-40*x-8 = -22.53061224

2/7

-2/7

x

-2/7

7*x^3-40*x^2-40*x-8 = 0

-2/7

x+2/7

7*x^2-42*x-28

7*x^3-40*x^2-40*x-8

x+2/7

-7*x^3-2*x^2

-42*x^2-40*x-8

42*x^2+12*x

-28*x-8

28*x+8

0

7*x^2-42*x-28 = 0

DELTA = (-42)^2-(-28*4*7)

DELTA = 2548

DELTA > 0

x = (2548^(1/2)+42)/(2*7) or x = (42-2548^(1/2))/(2*7)

x = (14*13^(1/2)+42)/14 or x = (42-14*13^(1/2))/14

x in { (42-14*13^(1/2))/14, (14*13^(1/2)+42)/14, -2/7} 

(x-((42-14*13^(1/2))/14))*(x-((14*13^(1/2)+42)/14))*(x+2/7) = 0

(7*x+2)/((x-((42-14*13^(1/2))/14))*(x-((14*13^(1/2)+42)/14))*(x+2/7)) = 0

7*x+2 = 0 // - 2

7*x = -2 // : 7

x = -2/7

x in { -2/7} 

x belongs to the empty set

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