(8x-9)(8x-9)=5

Solution for (8x-9)(8x-9)=5 equation:

Simplifying
(8x + -9)(8x + -9) = 5

Reorder the terms:
(-9 + 8x)(8x + -9) = 5

Reorder the terms:
(-9 + 8x)(-9 + 8x) = 5

Multiply (-9 + 8x) * (-9 + 8x)
(-9(-9 + 8x) + 8x * (-9 + 8x)) = 5
((-9 * -9 + 8x * -9) + 8x * (-9 + 8x)) = 5
((81 + -72x) + 8x * (-9 + 8x)) = 5
(81 + -72x + (-9 * 8x + 8x * 8x)) = 5
(81 + -72x + (-72x + 64x2)) = 5

Combine like terms: -72x + -72x = -144x
(81 + -144x + 64x2) = 5

Solving
81 + -144x + 64x2 = 5

Solving for variable 'x'.

Reorder the terms:
81 + -5 + -144x + 64x2 = 5 + -5

Combine like terms: 81 + -5 = 76
76 + -144x + 64x2 = 5 + -5

Combine like terms: 5 + -5 = 0
76 + -144x + 64x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(19 + -36x + 16x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(19 + -36x + 16x2)' equal to zero and attempt to solve:

Simplifying
19 + -36x + 16x2 = 0

Solving
19 + -36x + 16x2 = 0

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

Divide each side by '16'.
1.1875 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-1.1875' to each side of the equation.
1.1875 + -2.25x + -1.1875 + x2 = 0 + -1.1875

Reorder the terms:
1.1875 + -1.1875 + -2.25x + x2 = 0 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + -2.25x + x2 = 0 + -1.1875
-2.25x + x2 = 0 + -1.1875

Combine like terms: 0 + -1.1875 = -1.1875
-2.25x + x2 = -1.1875

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = -1.1875 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -1.1875 + 1.265625

Combine like terms: -1.1875 + 1.265625 = 0.078125
1.265625 + -2.25x + x2 = 0.078125

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 0.078125

Calculate the square root of the right side: 0.279508497

Break this problem into two subproblems by setting 
(x + -1.125) equal to 0.279508497 and -0.279508497.

Subproblem 1
x + -1.125 = 0.279508497

Simplifying
x + -1.125 = 0.279508497

Reorder the terms:
-1.125 + x = 0.279508497

Solving
-1.125 + x = 0.279508497

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 0.279508497 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 0.279508497 + 1.125
x = 0.279508497 + 1.125

Combine like terms: 0.279508497 + 1.125 = 1.404508497
x = 1.404508497

Simplifying
x = 1.404508497

Subproblem 2
x + -1.125 = -0.279508497

Simplifying
x + -1.125 = -0.279508497

Reorder the terms:
-1.125 + x = -0.279508497

Solving
-1.125 + x = -0.279508497

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -0.279508497 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -0.279508497 + 1.125
x = -0.279508497 + 1.125

Combine like terms: -0.279508497 + 1.125 = 0.845491503
x = 0.845491503

Simplifying
x = 0.845491503

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.404508497, 0.845491503}
Solution
x = {1.404508497, 0.845491503}