2(8x-1)(8x-1)=4

Solution for 2(8x-1)(8x-1)=4 equation:

Simplifying
2(8x + -1)(8x + -1) = 4

Reorder the terms:
2(-1 + 8x)(8x + -1) = 4

Reorder the terms:
2(-1 + 8x)(-1 + 8x) = 4

Multiply (-1 + 8x) * (-1 + 8x)
2(-1(-1 + 8x) + 8x * (-1 + 8x)) = 4
2((-1 * -1 + 8x * -1) + 8x * (-1 + 8x)) = 4
2((1 + -8x) + 8x * (-1 + 8x)) = 4
2(1 + -8x + (-1 * 8x + 8x * 8x)) = 4
2(1 + -8x + (-8x + 64x2)) = 4

Combine like terms: -8x + -8x = -16x
2(1 + -16x + 64x2) = 4
(1 * 2 + -16x * 2 + 64x2 * 2) = 4
(2 + -32x + 128x2) = 4

Solving
2 + -32x + 128x2 = 4

Solving for variable 'x'.

Reorder the terms:
2 + -4 + -32x + 128x2 = 4 + -4

Combine like terms: 2 + -4 = -2
-2 + -32x + 128x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-2 + -32x + 128x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -16x + 64x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -16x + 64x2)' equal to zero and attempt to solve:

Simplifying
-1 + -16x + 64x2 = 0

Solving
-1 + -16x + 64x2 = 0

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

Divide each side by '64'.
-0.015625 + -0.25x + x2 = 0

Move the constant term to the right:

Add '0.015625' to each side of the equation.
-0.015625 + -0.25x + 0.015625 + x2 = 0 + 0.015625

Reorder the terms:
-0.015625 + 0.015625 + -0.25x + x2 = 0 + 0.015625

Combine like terms: -0.015625 + 0.015625 = 0.000000
0.000000 + -0.25x + x2 = 0 + 0.015625
-0.25x + x2 = 0 + 0.015625

Combine like terms: 0 + 0.015625 = 0.015625
-0.25x + x2 = 0.015625

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 0.015625 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.015625 + 0.015625

Combine like terms: 0.015625 + 0.015625 = 0.03125
0.015625 + -0.25x + x2 = 0.03125

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.03125

Calculate the square root of the right side: 0.176776695

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.176776695 and -0.176776695.

Subproblem 1
x + -0.125 = 0.176776695

Simplifying
x + -0.125 = 0.176776695

Reorder the terms:
-0.125 + x = 0.176776695

Solving
-0.125 + x = 0.176776695

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = 0.176776695 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 0.176776695 + 0.125
x = 0.176776695 + 0.125

Combine like terms: 0.176776695 + 0.125 = 0.301776695
x = 0.301776695

Simplifying
x = 0.301776695

Subproblem 2
x + -0.125 = -0.176776695

Simplifying
x + -0.125 = -0.176776695

Reorder the terms:
-0.125 + x = -0.176776695

Solving
-0.125 + x = -0.176776695

Solving for variable 'x'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + x = -0.176776695 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -0.176776695 + 0.125
x = -0.176776695 + 0.125

Combine like terms: -0.176776695 + 0.125 = -0.051776695
x = -0.051776695

Simplifying
x = -0.051776695

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.301776695, -0.051776695}
Solution
x = {0.301776695, -0.051776695}