0.01(x-8)(x-3)(x+8)(x+3)=5

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Solution for 0.01(x-8)(x-3)(x+8)(x+3)=5 equation: 


Simplifying
0.01(x + -8)(x + -3)(x + 8)(x + 3) = 5

Reorder the terms:
0.01(-8 + x)(x + -3)(x + 8)(x + 3) = 5

Reorder the terms:
0.01(-8 + x)(-3 + x)(x + 8)(x + 3) = 5

Reorder the terms:
0.01(-8 + x)(-3 + x)(8 + x)(x + 3) = 5

Reorder the terms:
0.01(-8 + x)(-3 + x)(8 + x)(3 + x) = 5

Multiply (-8 + x) * (-3 + x)
0.01(-8(-3 + x) + x(-3 + x))(8 + x)(3 + x) = 5
0.01((-3 * -8 + x * -8) + x(-3 + x))(8 + x)(3 + x) = 5
0.01((24 + -8x) + x(-3 + x))(8 + x)(3 + x) = 5
0.01(24 + -8x + (-3 * x + x * x))(8 + x)(3 + x) = 5
0.01(24 + -8x + (-3x + x2))(8 + x)(3 + x) = 5

Combine like terms: -8x + -3x = -11x
0.01(24 + -11x + x2)(8 + x)(3 + x) = 5

Multiply (24 + -11x + x2) * (8 + x)
0.01(24(8 + x) + -11x * (8 + x) + x2(8 + x))(3 + x) = 5
0.01((8 * 24 + x * 24) + -11x * (8 + x) + x2(8 + x))(3 + x) = 5
0.01((192 + 24x) + -11x * (8 + x) + x2(8 + x))(3 + x) = 5
0.01(192 + 24x + (8 * -11x + x * -11x) + x2(8 + x))(3 + x) = 5
0.01(192 + 24x + (-88x + -11x2) + x2(8 + x))(3 + x) = 5
0.01(192 + 24x + -88x + -11x2 + (8 * x2 + x * x2))(3 + x) = 5
0.01(192 + 24x + -88x + -11x2 + (8x2 + x3))(3 + x) = 5

Combine like terms: 24x + -88x = -64x
0.01(192 + -64x + -11x2 + 8x2 + x3)(3 + x) = 5

Combine like terms: -11x2 + 8x2 = -3x2
0.01(192 + -64x + -3x2 + x3)(3 + x) = 5

Multiply (192 + -64x + -3x2 + x3) * (3 + x)
0.01(192(3 + x) + -64x * (3 + x) + -3x2 * (3 + x) + x3(3 + x)) = 5
0.01((3 * 192 + x * 192) + -64x * (3 + x) + -3x2 * (3 + x) + x3(3 + x)) = 5
0.01((576 + 192x) + -64x * (3 + x) + -3x2 * (3 + x) + x3(3 + x)) = 5
0.01(576 + 192x + (3 * -64x + x * -64x) + -3x2 * (3 + x) + x3(3 + x)) = 5
0.01(576 + 192x + (-192x + -64x2) + -3x2 * (3 + x) + x3(3 + x)) = 5
0.01(576 + 192x + -192x + -64x2 + (3 * -3x2 + x * -3x2) + x3(3 + x)) = 5
0.01(576 + 192x + -192x + -64x2 + (-9x2 + -3x3) + x3(3 + x)) = 5
0.01(576 + 192x + -192x + -64x2 + -9x2 + -3x3 + (3 * x3 + x * x3)) = 5
0.01(576 + 192x + -192x + -64x2 + -9x2 + -3x3 + (3x3 + x4)) = 5

Combine like terms: 192x + -192x = 0
0.01(576 + 0 + -64x2 + -9x2 + -3x3 + 3x3 + x4) = 5
0.01(576 + -64x2 + -9x2 + -3x3 + 3x3 + x4) = 5

Combine like terms: -64x2 + -9x2 = -73x2
0.01(576 + -73x2 + -3x3 + 3x3 + x4) = 5

Combine like terms: -3x3 + 3x3 = 0
0.01(576 + -73x2 + 0 + x4) = 5
0.01(576 + -73x2 + x4) = 5
(576 * 0.01 + -73x2 * 0.01 + x4 * 0.01) = 5
(5.76 + -0.73x2 + 0.01x4) = 5

Solving
5.76 + -0.73x2 + 0.01x4 = 5

Solving for variable 'x'.

Reorder the terms:
5.76 + -5 + -0.73x2 + 0.01x4 = 5 + -5

Combine like terms: 5.76 + -5 = 0.76
0.76 + -0.73x2 + 0.01x4 = 5 + -5

Combine like terms: 5 + -5 = 0
0.76 + -0.73x2 + 0.01x4 = 0

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

Divide each side by '0.01'.
76 + -73x2 + x4 = 0

Move the constant term to the right:

Add '-76' to each side of the equation.
76 + -73x2 + -76 + x4 = 0 + -76

Reorder the terms:
76 + -76 + -73x2 + x4 = 0 + -76

Combine like terms: 76 + -76 = 0
0 + -73x2 + x4 = 0 + -76
-73x2 + x4 = 0 + -76

Combine like terms: 0 + -76 = -76
-73x2 + x4 = -76

The x term is -73x2.  Take half its coefficient (-36.5).
Square it (1332.25) and add it to both sides.

Add '1332.25' to each side of the equation.
-73x2 + 1332.25 + x4 = -76 + 1332.25

Reorder the terms:
1332.25 + -73x2 + x4 = -76 + 1332.25

Combine like terms: -76 + 1332.25 = 1256.25
1332.25 + -73x2 + x4 = 1256.25

Factor a perfect square on the left side:
(x2 + -36.5)(x2 + -36.5) = 1256.25

Calculate the square root of the right side: 35.443617197

Break this problem into two subproblems by setting 
(x2 + -36.5) equal to 35.443617197 and -35.443617197.


Subproblem 1
x2 + -36.5 = 35.443617197

Simplifying
x2 + -36.5 = 35.443617197

Reorder the terms:
-36.5 + x2 = 35.443617197

Solving
-36.5 + x2 = 35.443617197

Solving for variable 'x'.

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

Add '36.5' to each side of the equation.
-36.5 + 36.5 + x2 = 35.443617197 + 36.5

Combine like terms: -36.5 + 36.5 = 0.0
0.0 + x2 = 35.443617197 + 36.5
x2 = 35.443617197 + 36.5

Combine like terms: 35.443617197 + 36.5 = 71.943617197
x2 = 71.943617197

Simplifying
x2 = 71.943617197

Take the square root of each side:
x = {-8.481958335, 8.481958335}


Subproblem 2
x2 + -36.5 = -35.443617197

Simplifying
x2 + -36.5 = -35.443617197

Reorder the terms:
-36.5 + x2 = -35.443617197

Solving
-36.5 + x2 = -35.443617197

Solving for variable 'x'.

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

Add '36.5' to each side of the equation.
-36.5 + 36.5 + x2 = -35.443617197 + 36.5

Combine like terms: -36.5 + 36.5 = 0.0
0.0 + x2 = -35.443617197 + 36.5
x2 = -35.443617197 + 36.5

Combine like terms: -35.443617197 + 36.5 = 1.056382803
x2 = 1.056382803

Simplifying
x2 = 1.056382803

Take the square root of each side:
x = {-1.027804847, 1.027804847}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.481958335, 8.481958335, -1.027804847, 1.027804847}

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