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

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

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

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

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

Multiply (-3 + 8x) * (-3 + 8x)
(-3(-3 + 8x) + 8x * (-3 + 8x)) = 5
((-3 * -3 + 8x * -3) + 8x * (-3 + 8x)) = 5
((9 + -24x) + 8x * (-3 + 8x)) = 5
(9 + -24x + (-3 * 8x + 8x * 8x)) = 5
(9 + -24x + (-24x + 64x2)) = 5

Combine like terms: -24x + -24x = -48x
(9 + -48x + 64x2) = 5

Solving
9 + -48x + 64x2 = 5

Solving for variable 'x'.

Reorder the terms:
9 + -5 + -48x + 64x2 = 5 + -5

Combine like terms: 9 + -5 = 4
4 + -48x + 64x2 = 5 + -5

Combine like terms: 5 + -5 = 0
4 + -48x + 64x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -12x + 16x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -12x + 16x2)' equal to zero and attempt to solve:

Simplifying
1 + -12x + 16x2 = 0

Solving
1 + -12x + 16x2 = 0

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

Divide each side by '16'.
0.0625 + -0.75x + x2 = 0

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + -0.75x + -0.0625 + x2 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + -0.75x + x2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + -0.75x + x2 = 0 + -0.0625
-0.75x + x2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
-0.75x + x2 = -0.0625

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = -0.0625 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = -0.0625 + 0.140625

Combine like terms: -0.0625 + 0.140625 = 0.078125
0.140625 + -0.75x + x2 = 0.078125

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.078125

Calculate the square root of the right side: 0.279508497

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.279508497 and -0.279508497.

Subproblem 1
x + -0.375 = 0.279508497

Simplifying
x + -0.375 = 0.279508497

Reorder the terms:
-0.375 + x = 0.279508497

Solving
-0.375 + x = 0.279508497

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 0.279508497 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 0.279508497 + 0.375
x = 0.279508497 + 0.375

Combine like terms: 0.279508497 + 0.375 = 0.654508497
x = 0.654508497

Simplifying
x = 0.654508497

Subproblem 2
x + -0.375 = -0.279508497

Simplifying
x + -0.375 = -0.279508497

Reorder the terms:
-0.375 + x = -0.279508497

Solving
-0.375 + x = -0.279508497

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -0.279508497 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -0.279508497 + 0.375
x = -0.279508497 + 0.375

Combine like terms: -0.279508497 + 0.375 = 0.095491503
x = 0.095491503

Simplifying
x = 0.095491503

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.654508497, 0.095491503}
Solution
x = {0.654508497, 0.095491503}