(x-2)(x+2)(-x-2)(-x+2)-8=0

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Solution for (x-2)(x+2)(-x-2)(-x+2)-8=0 equation: 


Simplifying
(x + -2)(x + 2)(-1x + -2)(-1x + 2) + -8 = 0

Reorder the terms:
(-2 + x)(x + 2)(-1x + -2)(-1x + 2) + -8 = 0

Reorder the terms:
(-2 + x)(2 + x)(-1x + -2)(-1x + 2) + -8 = 0

Reorder the terms:
(-2 + x)(2 + x)(-2 + -1x)(-1x + 2) + -8 = 0

Reorder the terms:
(-2 + x)(2 + x)(-2 + -1x)(2 + -1x) + -8 = 0

Multiply (-2 + x) * (2 + x)
(-2(2 + x) + x(2 + x))(-2 + -1x)(2 + -1x) + -8 = 0
((2 * -2 + x * -2) + x(2 + x))(-2 + -1x)(2 + -1x) + -8 = 0
((-4 + -2x) + x(2 + x))(-2 + -1x)(2 + -1x) + -8 = 0
(-4 + -2x + (2 * x + x * x))(-2 + -1x)(2 + -1x) + -8 = 0
(-4 + -2x + (2x + x2))(-2 + -1x)(2 + -1x) + -8 = 0

Combine like terms: -2x + 2x = 0
(-4 + 0 + x2)(-2 + -1x)(2 + -1x) + -8 = 0
(-4 + x2)(-2 + -1x)(2 + -1x) + -8 = 0

Multiply (-4 + x2) * (-2 + -1x)
(-4(-2 + -1x) + x2(-2 + -1x))(2 + -1x) + -8 = 0
((-2 * -4 + -1x * -4) + x2(-2 + -1x))(2 + -1x) + -8 = 0
((8 + 4x) + x2(-2 + -1x))(2 + -1x) + -8 = 0
(8 + 4x + (-2 * x2 + -1x * x2))(2 + -1x) + -8 = 0
(8 + 4x + (-2x2 + -1x3))(2 + -1x) + -8 = 0
(8 + 4x + -2x2 + -1x3)(2 + -1x) + -8 = 0

Multiply (8 + 4x + -2x2 + -1x3) * (2 + -1x)
(8(2 + -1x) + 4x * (2 + -1x) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) + -8 = 0
((2 * 8 + -1x * 8) + 4x * (2 + -1x) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) + -8 = 0
((16 + -8x) + 4x * (2 + -1x) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) + -8 = 0
(16 + -8x + (2 * 4x + -1x * 4x) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) + -8 = 0
(16 + -8x + (8x + -4x2) + -2x2 * (2 + -1x) + -1x3 * (2 + -1x)) + -8 = 0
(16 + -8x + 8x + -4x2 + (2 * -2x2 + -1x * -2x2) + -1x3 * (2 + -1x)) + -8 = 0
(16 + -8x + 8x + -4x2 + (-4x2 + 2x3) + -1x3 * (2 + -1x)) + -8 = 0
(16 + -8x + 8x + -4x2 + -4x2 + 2x3 + (2 * -1x3 + -1x * -1x3)) + -8 = 0
(16 + -8x + 8x + -4x2 + -4x2 + 2x3 + (-2x3 + 1x4)) + -8 = 0

Combine like terms: -8x + 8x = 0
(16 + 0 + -4x2 + -4x2 + 2x3 + -2x3 + 1x4) + -8 = 0
(16 + -4x2 + -4x2 + 2x3 + -2x3 + 1x4) + -8 = 0

Combine like terms: -4x2 + -4x2 = -8x2
(16 + -8x2 + 2x3 + -2x3 + 1x4) + -8 = 0

Combine like terms: 2x3 + -2x3 = 0
(16 + -8x2 + 0 + 1x4) + -8 = 0
(16 + -8x2 + 1x4) + -8 = 0

Reorder the terms:
16 + -8 + -8x2 + 1x4 = 0

Combine like terms: 16 + -8 = 8
8 + -8x2 + 1x4 = 0

Solving
8 + -8x2 + 1x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -8x2 + -8 + x4 = 0 + -8

Reorder the terms:
8 + -8 + -8x2 + x4 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -8x2 + x4 = 0 + -8
-8x2 + x4 = 0 + -8

Combine like terms: 0 + -8 = -8
-8x2 + x4 = -8

The x term is -8x2.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x2 + 16 + x4 = -8 + 16

Reorder the terms:
16 + -8x2 + x4 = -8 + 16

Combine like terms: -8 + 16 = 8
16 + -8x2 + x4 = 8

Factor a perfect square on the left side:
(x2 + -4)(x2 + -4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x2 + -4) equal to 2.828427125 and -2.828427125.


Subproblem 1
x2 + -4 = 2.828427125

Simplifying
x2 + -4 = 2.828427125

Reorder the terms:
-4 + x2 = 2.828427125

Solving
-4 + x2 = 2.828427125

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = 2.828427125 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = 2.828427125 + 4
x2 = 2.828427125 + 4

Combine like terms: 2.828427125 + 4 = 6.828427125
x2 = 6.828427125

Simplifying
x2 = 6.828427125

Take the square root of each side:
x = {-2.61312593, 2.61312593}


Subproblem 2
x2 + -4 = -2.828427125

Simplifying
x2 + -4 = -2.828427125

Reorder the terms:
-4 + x2 = -2.828427125

Solving
-4 + x2 = -2.828427125

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = -2.828427125 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = -2.828427125 + 4
x2 = -2.828427125 + 4

Combine like terms: -2.828427125 + 4 = 1.171572875
x2 = 1.171572875

Simplifying
x2 = 1.171572875

Take the square root of each side:
x = {-1.0823922, 1.0823922}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.61312593, 2.61312593, -1.0823922, 1.0823922}

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