(16x^5-32x^4-81x+162)/(2x-3)

Simple and best practice solution for (16x^5-32x^4-81x+162)/(2x-3) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

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Solution for (16x^5-32x^4-81x+162)/(2x-3) equation:

D( x )

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

x in (-oo:3/2) U (3/2:+oo)

(16*x^5-(32*x^4)-(81*x)+162)/(2*x-3) = 0

(16*x^5-32*x^4-81*x+162)/(2*x-3) = 0

16*x^5-32*x^4-81*x+162 = 0

16*x^5-32*x^4-81*x+162 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18, 27, -27, 54, -54, 81, -81, 162, -162 }

1

x = 1

16*x^5-32*x^4-81*x+162 = 65

1

-1

x = -1

16*x^5-32*x^4-81*x+162 = 195

-1

2

x = 2

16*x^5-32*x^4-81*x+162 = 0

2

x-2

16*x^4-81

16*x^5-32*x^4-81*x+162

x-2

32*x^4-16*x^5

162-81*x

81*x-162

0

16*x^4-81 = 0

{ 1, -1, 3, -3, 9, -9, 27, -27, 81, -81 }

1

x = 1

16*x^4-81 = -65

1

-1

x = -1

16*x^4-81 = -65

-1

3

x = 3

16*x^4-81 = 1215

3

-3

x = -3

16*x^4-81 = 1215

-3

9

x = 9

16*x^4-81 = 104895

9

-9

x = -9

16*x^4-81 = 104895

-9

27

x = 27

16*x^4-81 = 8502975

27

-27

x = -27

16*x^4-81 = 8502975

-27

81

x = 81

16*x^4-81 = 688747455

81

-81

x = -81

16*x^4-81 = 688747455

-81

{ 1/2, -1/2, 1/4, -1/4, 1/8, -1/8, 1/16, -1/16, -1/2, 1/2, -1/4, 1/4, -1/8, 1/8, -1/16, 1/16, 3/2, -3/2, 3/4, -3/4, 3/8, -3/8, 3/16, -3/16, -3/2, 3/2, -3/4, 3/4, -3/8, 3/8, -3/16, 3/16, 9/2, -9/2, 9/4, -9/4, 9/8, -9/8, 9/16, -9/16, -9/2, 9/2, -9/4, 9/4, -9/8, 9/8, -9/16, 9/16, 27/2, -27/2, 27/4, -27/4, 27/8, -27/8, 27/16, -27/16, -27/2, 27/2, -27/4, 27/4, -27/8, 27/8, -27/16, 27/16, 81/2, -81/2, 81/4, -81/4, 81/8, -81/8, 81/16, -81/16, -81/2, 81/2, -81/4, 81/4, -81/8, 81/8, -81/16, 81/16 }

1/2

x

1/2

16*x^4-81 = -80

1/2

-1/2

x

-1/2

16*x^4-81 = -80

-1/2

1/4

x

1/4

16*x^4-81 = -80.9375

1/4

-1/4

x

-1/4

16*x^4-81 = -80.9375

-1/4

1/8

x

1/8

16*x^4-81 = -80.99609375

1/8

-1/8

x

-1/8

16*x^4-81 = -80.99609375

-1/8

1/16

x

1/16

16*x^4-81 = -80.99975586

1/16

-1/16

x

-1/16

16*x^4-81 = -80.99975586

-1/16

-1/2

x

-1/2

16*x^4-81 = -80

-1/2

1/2

x

1/2

16*x^4-81 = -80

1/2

-1/4

x

-1/4

16*x^4-81 = -80.9375

-1/4

1/4

x

1/4

16*x^4-81 = -80.9375

1/4

-1/8

x

-1/8

16*x^4-81 = -80.99609375

-1/8

1/8

x

1/8

16*x^4-81 = -80.99609375

1/8

-1/16

x

-1/16

16*x^4-81 = -80.99975586

-1/16

1/16

x

1/16

16*x^4-81 = -80.99975586

1/16

3/2

x

3/2

16*x^4-81 = 0

3/2

x-3/2

16*x^3+24*x^2+36*x+54

16*x^4-81

x-3/2

24*x^3-16*x^4

24*x^3-81

36*x^2-24*x^3

36*x^2-81

54*x-36*x^2

54*x-81

81-54*x

0

16*x^3+24*x^2+36*x+54 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18, 27, -27, 54, -54 }

1

x = 1

16*x^3+24*x^2+36*x+54 = 130

1

-1

x = -1

16*x^3+24*x^2+36*x+54 = 26

-1

2

x = 2

16*x^3+24*x^2+36*x+54 = 350

2

-2

x = -2

16*x^3+24*x^2+36*x+54 = -50

-2

3

x = 3

16*x^3+24*x^2+36*x+54 = 810

3

-3

x = -3

16*x^3+24*x^2+36*x+54 = -270

-3

6

x = 6

16*x^3+24*x^2+36*x+54 = 4590

6

-6

x = -6

16*x^3+24*x^2+36*x+54 = -2754

-6

9

x = 9

16*x^3+24*x^2+36*x+54 = 13986

9

-9

x = -9

16*x^3+24*x^2+36*x+54 = -9990

-9

18

x = 18

16*x^3+24*x^2+36*x+54 = 101790

18

-18

x = -18

16*x^3+24*x^2+36*x+54 = -86130

-18

27

x = 27

16*x^3+24*x^2+36*x+54 = 333450

27

-27

x = -27

16*x^3+24*x^2+36*x+54 = -298350

-27

54

x = 54

16*x^3+24*x^2+36*x+54 = 2591406

54

-54

x = -54

16*x^3+24*x^2+36*x+54 = -2451330

-54

{ 1/2, -1/2, 1/4, -1/4, 1/8, -1/8, 1/16, -1/16, -1/2, 1/2, -1/4, 1/4, -1/8, 1/8, -1/16, 1/16, 2/2, -2/2, 2/4, -2/4, 2/8, -2/8, 2/16, -2/16, -2/2, 2/2, -2/4, 2/4, -2/8, 2/8, -2/16, 2/16, 3/2, -3/2, 3/4, -3/4, 3/8, -3/8, 3/16, -3/16, -3/2, 3/2, -3/4, 3/4, -3/8, 3/8, -3/16, 3/16, 6/2, -6/2, 6/4, -6/4, 6/8, -6/8, 6/16, -6/16, -6/2, 6/2, -6/4, 6/4, -6/8, 6/8, -6/16, 6/16, 9/2, -9/2, 9/4, -9/4, 9/8, -9/8, 9/16, -9/16, -9/2, 9/2, -9/4, 9/4, -9/8, 9/8, -9/16, 9/16, 18/2, -18/2, 18/4, -18/4, 18/8, -18/8, 18/16, -18/16, -18/2, 18/2, -18/4, 18/4, -18/8, 18/8, -18/16, 18/16, 27/2, -27/2, 27/4, -27/4, 27/8, -27/8, 27/16, -27/16, -27/2, 27/2, -27/4, 27/4, -27/8, 27/8, -27/16, 27/16, 54/2, -54/2, 54/4, -54/4, 54/8, -54/8, 54/16, -54/16, -54/2, 54/2, -54/4, 54/4, -54/8, 54/8, -54/16, 54/16 }

1/2

x

1/2

16*x^3+24*x^2+36*x+54 = 80

1/2

-1/2

x

-1/2

16*x^3+24*x^2+36*x+54 = 40

-1/2

1/4

x

1/4

16*x^3+24*x^2+36*x+54 = 64.75

1/4

-1/4

x

-1/4

16*x^3+24*x^2+36*x+54 = 46.25

-1/4

1/8

x

1/8

16*x^3+24*x^2+36*x+54 = 58.90625

1/8

-1/8

x

-1/8

16*x^3+24*x^2+36*x+54 = 49.84375

-1/8

1/16

x

1/16

16*x^3+24*x^2+36*x+54 = 56.34765625

1/16

-1/16

x

-1/16

16*x^3+24*x^2+36*x+54 = 51.83984375

-1/16

-1/2

x

-1/2

16*x^3+24*x^2+36*x+54 = 40

-1/2

1/2

x

1/2

16*x^3+24*x^2+36*x+54 = 80

1/2

-1/4

x

-1/4

16*x^3+24*x^2+36*x+54 = 46.25

-1/4

1/4

x

1/4

16*x^3+24*x^2+36*x+54 = 64.75

1/4

-1/8

x

-1/8

16*x^3+24*x^2+36*x+54 = 49.84375

-1/8

1/8

x

1/8

16*x^3+24*x^2+36*x+54 = 58.90625

1/8

-1/16

x

-1/16

16*x^3+24*x^2+36*x+54 = 51.83984375

-1/16

1/16

x

1/16

16*x^3+24*x^2+36*x+54 = 56.34765625

1/16

2/2

x

2/2

16*x^3+24*x^2+36*x+54 = 130

2/2

-2/2

x

-2/2

16*x^3+24*x^2+36*x+54 = 26

-2/2

2/4

x

2/4

16*x^3+24*x^2+36*x+54 = 80

2/4

-2/4

x

-2/4

16*x^3+24*x^2+36*x+54 = 40

-2/4

2/8

x

2/8

16*x^3+24*x^2+36*x+54 = 64.75

2/8

-2/8

x

-2/8

16*x^3+24*x^2+36*x+54 = 46.25

-2/8

2/16

x

2/16

16*x^3+24*x^2+36*x+54 = 58.90625

2/16

-2/16

x

-2/16

16*x^3+24*x^2+36*x+54 = 49.84375

-2/16

-2/2

x

-2/2

16*x^3+24*x^2+36*x+54 = 26

-2/2

2/2

x

2/2

16*x^3+24*x^2+36*x+54 = 130

2/2

-2/4

x

-2/4

16*x^3+24*x^2+36*x+54 = 40

-2/4

2/4

x

2/4

16*x^3+24*x^2+36*x+54 = 80

2/4

-2/8

x

-2/8

16*x^3+24*x^2+36*x+54 = 46.25

-2/8

2/8

x

2/8

16*x^3+24*x^2+36*x+54 = 64.75

2/8

-2/16

x

-2/16

16*x^3+24*x^2+36*x+54 = 49.84375

-2/16

2/16

x

2/16

16*x^3+24*x^2+36*x+54 = 58.90625

2/16

3/2

x

3/2

16*x^3+24*x^2+36*x+54 = 216

3/2

-3/2

x

-3/2

16*x^3+24*x^2+36*x+54 = 0

-3/2

x+3/2

16*x^2+36

16*x^3+24*x^2+36*x+54

x+3/2

-16*x^3-24*x^2

36*x+54

-36*x-54

0

16*x^2+36 = 0

DELTA = 0^2-(4*16*36)

DELTA = -2304

DELTA < 0

x in { 2, 3/2, -3/2} 

(x-2)*(x-3/2)*(x+3/2) = 0

((x-2)*(x-3/2)*(x+3/2))/(2*x-3) = 0

( x+3/2 )

x+3/2 = 0 // - 3/2

x = -3/2

( x-2 )

x-2 = 0 // + 2

x = 2

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

x in { 3/2} 

x in { -3/2, 2 }

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(16x^5-32x^4-81x+162)/(2x-3)

Simple and best practice solution for (16x^5-32x^4-81x+162)/(2x-3) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

Solution for (16x^5-32x^4-81x+162)/(2x-3) equation:

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