-3(x-5)(x+5)(x-8)(x+8)-1=0

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Solution for -3(x-5)(x+5)(x-8)(x+8)-1=0 equation:


Simplifying
-3(x + -5)(x + 5)(x + -8)(x + 8) + -1 = 0

Reorder the terms:
-3(-5 + x)(x + 5)(x + -8)(x + 8) + -1 = 0

Reorder the terms:
-3(-5 + x)(5 + x)(x + -8)(x + 8) + -1 = 0

Reorder the terms:
-3(-5 + x)(5 + x)(-8 + x)(x + 8) + -1 = 0

Reorder the terms:
-3(-5 + x)(5 + x)(-8 + x)(8 + x) + -1 = 0

Multiply (-5 + x) * (5 + x)
-3(-5(5 + x) + x(5 + x))(-8 + x)(8 + x) + -1 = 0
-3((5 * -5 + x * -5) + x(5 + x))(-8 + x)(8 + x) + -1 = 0
-3((-25 + -5x) + x(5 + x))(-8 + x)(8 + x) + -1 = 0
-3(-25 + -5x + (5 * x + x * x))(-8 + x)(8 + x) + -1 = 0
-3(-25 + -5x + (5x + x2))(-8 + x)(8 + x) + -1 = 0

Combine like terms: -5x + 5x = 0
-3(-25 + 0 + x2)(-8 + x)(8 + x) + -1 = 0
-3(-25 + x2)(-8 + x)(8 + x) + -1 = 0

Multiply (-25 + x2) * (-8 + x)
-3(-25(-8 + x) + x2(-8 + x))(8 + x) + -1 = 0
-3((-8 * -25 + x * -25) + x2(-8 + x))(8 + x) + -1 = 0
-3((200 + -25x) + x2(-8 + x))(8 + x) + -1 = 0
-3(200 + -25x + (-8 * x2 + x * x2))(8 + x) + -1 = 0
-3(200 + -25x + (-8x2 + x3))(8 + x) + -1 = 0
-3(200 + -25x + -8x2 + x3)(8 + x) + -1 = 0

Multiply (200 + -25x + -8x2 + x3) * (8 + x)
-3(200(8 + x) + -25x * (8 + x) + -8x2 * (8 + x) + x3(8 + x)) + -1 = 0
-3((8 * 200 + x * 200) + -25x * (8 + x) + -8x2 * (8 + x) + x3(8 + x)) + -1 = 0
-3((1600 + 200x) + -25x * (8 + x) + -8x2 * (8 + x) + x3(8 + x)) + -1 = 0
-3(1600 + 200x + (8 * -25x + x * -25x) + -8x2 * (8 + x) + x3(8 + x)) + -1 = 0
-3(1600 + 200x + (-200x + -25x2) + -8x2 * (8 + x) + x3(8 + x)) + -1 = 0
-3(1600 + 200x + -200x + -25x2 + (8 * -8x2 + x * -8x2) + x3(8 + x)) + -1 = 0
-3(1600 + 200x + -200x + -25x2 + (-64x2 + -8x3) + x3(8 + x)) + -1 = 0
-3(1600 + 200x + -200x + -25x2 + -64x2 + -8x3 + (8 * x3 + x * x3)) + -1 = 0
-3(1600 + 200x + -200x + -25x2 + -64x2 + -8x3 + (8x3 + x4)) + -1 = 0

Combine like terms: 200x + -200x = 0
-3(1600 + 0 + -25x2 + -64x2 + -8x3 + 8x3 + x4) + -1 = 0
-3(1600 + -25x2 + -64x2 + -8x3 + 8x3 + x4) + -1 = 0

Combine like terms: -25x2 + -64x2 = -89x2
-3(1600 + -89x2 + -8x3 + 8x3 + x4) + -1 = 0

Combine like terms: -8x3 + 8x3 = 0
-3(1600 + -89x2 + 0 + x4) + -1 = 0
-3(1600 + -89x2 + x4) + -1 = 0
(1600 * -3 + -89x2 * -3 + x4 * -3) + -1 = 0
(-4800 + 267x2 + -3x4) + -1 = 0

Reorder the terms:
-4800 + -1 + 267x2 + -3x4 = 0

Combine like terms: -4800 + -1 = -4801
-4801 + 267x2 + -3x4 = 0

Solving
-4801 + 267x2 + -3x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1600.333333 + -89x2 + x4 = 0

Move the constant term to the right:

Add '-1600.333333' to each side of the equation.
1600.333333 + -89x2 + -1600.333333 + x4 = 0 + -1600.333333

Reorder the terms:
1600.333333 + -1600.333333 + -89x2 + x4 = 0 + -1600.333333

Combine like terms: 1600.333333 + -1600.333333 = 0.000000
0.000000 + -89x2 + x4 = 0 + -1600.333333
-89x2 + x4 = 0 + -1600.333333

Combine like terms: 0 + -1600.333333 = -1600.333333
-89x2 + x4 = -1600.333333

The x term is -89x2.  Take half its coefficient (-44.5).
Square it (1980.25) and add it to both sides.

Add '1980.25' to each side of the equation.
-89x2 + 1980.25 + x4 = -1600.333333 + 1980.25

Reorder the terms:
1980.25 + -89x2 + x4 = -1600.333333 + 1980.25

Combine like terms: -1600.333333 + 1980.25 = 379.916667
1980.25 + -89x2 + x4 = 379.916667

Factor a perfect square on the left side:
(x2 + -44.5)(x2 + -44.5) = 379.916667

Calculate the square root of the right side: 19.491451126

Break this problem into two subproblems by setting 
(x2 + -44.5) equal to 19.491451126 and -19.491451126.


Subproblem 1
x2 + -44.5 = 19.491451126

Simplifying
x2 + -44.5 = 19.491451126

Reorder the terms:
-44.5 + x2 = 19.491451126

Solving
-44.5 + x2 = 19.491451126

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '44.5' to each side of the equation.
-44.5 + 44.5 + x2 = 19.491451126 + 44.5

Combine like terms: -44.5 + 44.5 = 0.0
0.0 + x2 = 19.491451126 + 44.5
x2 = 19.491451126 + 44.5

Combine like terms: 19.491451126 + 44.5 = 63.991451126
x2 = 63.991451126

Simplifying
x2 = 63.991451126

Take the square root of each side:
x = {-7.999465678, 7.999465678}


Subproblem 2
x2 + -44.5 = -19.491451126

Simplifying
x2 + -44.5 = -19.491451126

Reorder the terms:
-44.5 + x2 = -19.491451126

Solving
-44.5 + x2 = -19.491451126

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '44.5' to each side of the equation.
-44.5 + 44.5 + x2 = -19.491451126 + 44.5

Combine like terms: -44.5 + 44.5 = 0.0
0.0 + x2 = -19.491451126 + 44.5
x2 = -19.491451126 + 44.5

Combine like terms: -19.491451126 + 44.5 = 25.008548874
x2 = 25.008548874

Simplifying
x2 = 25.008548874

Take the square root of each side:
x = {-5.000854814, 5.000854814}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-7.999465678, 7.999465678, -5.000854814, 5.000854814}

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