(4x-8)(4x-8)=66

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Solution for (4x-8)(4x-8)=66 equation: 


Simplifying
(4x + -8)(4x + -8) = 66

Reorder the terms:
(-8 + 4x)(4x + -8) = 66

Reorder the terms:
(-8 + 4x)(-8 + 4x) = 66

Multiply (-8 + 4x) * (-8 + 4x)
(-8(-8 + 4x) + 4x * (-8 + 4x)) = 66
((-8 * -8 + 4x * -8) + 4x * (-8 + 4x)) = 66
((64 + -32x) + 4x * (-8 + 4x)) = 66
(64 + -32x + (-8 * 4x + 4x * 4x)) = 66
(64 + -32x + (-32x + 16x2)) = 66

Combine like terms: -32x + -32x = -64x
(64 + -64x + 16x2) = 66

Solving
64 + -64x + 16x2 = 66

Solving for variable 'x'.

Reorder the terms:
64 + -66 + -64x + 16x2 = 66 + -66

Combine like terms: 64 + -66 = -2
-2 + -64x + 16x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-2 + -64x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -32x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -32x + 8x2)' equal to zero and attempt to solve:

Simplifying
-1 + -32x + 8x2 = 0

Solving
-1 + -32x + 8x2 = 0

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

Divide each side by '8'.
-0.125 + -4x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -4x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -4x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -4x + x2 = 0 + 0.125
-4x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-4x + x2 = 0.125

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 0.125 + 4

Reorder the terms:
4 + -4x + x2 = 0.125 + 4

Combine like terms: 0.125 + 4 = 4.125
4 + -4x + x2 = 4.125

Factor a perfect square on the left side:
(x + -2)(x + -2) = 4.125

Calculate the square root of the right side: 2.031009601

Break this problem into two subproblems by setting 
(x + -2) equal to 2.031009601 and -2.031009601.


Subproblem 1
x + -2 = 2.031009601

Simplifying
x + -2 = 2.031009601

Reorder the terms:
-2 + x = 2.031009601

Solving
-2 + x = 2.031009601

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.031009601 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.031009601 + 2
x = 2.031009601 + 2

Combine like terms: 2.031009601 + 2 = 4.031009601
x = 4.031009601

Simplifying
x = 4.031009601


Subproblem 2
x + -2 = -2.031009601

Simplifying
x + -2 = -2.031009601

Reorder the terms:
-2 + x = -2.031009601

Solving
-2 + x = -2.031009601

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.031009601 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.031009601 + 2
x = -2.031009601 + 2

Combine like terms: -2.031009601 + 2 = -0.031009601
x = -0.031009601

Simplifying
x = -0.031009601


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.031009601, -0.031009601}
Solution
x = {4.031009601, -0.031009601}

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