(2x-9)8x=1

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Solution for (2x-9)8x=1 equation: 


Simplifying
(2x + -9) * 8x = 1

Reorder the terms:
(-9 + 2x) * 8x = 1

Reorder the terms for easier multiplication:
8x(-9 + 2x) = 1
(-9 * 8x + 2x * 8x) = 1
(-72x + 16x2) = 1

Solving
-72x + 16x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + -72x + 16x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -72x + 16x2 = 0

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

Divide each side by '16'.
-0.0625 + -4.5x + x2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + -4.5x + 0.0625 + x2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + -4.5x + x2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + -4.5x + x2 = 0 + 0.0625
-4.5x + x2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
-4.5x + x2 = 0.0625

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 0.0625 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 0.0625 + 5.0625

Combine like terms: 0.0625 + 5.0625 = 5.125
5.0625 + -4.5x + x2 = 5.125

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 5.125

Calculate the square root of the right side: 2.263846285

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.263846285 and -2.263846285.


Subproblem 1
x + -2.25 = 2.263846285

Simplifying
x + -2.25 = 2.263846285

Reorder the terms:
-2.25 + x = 2.263846285

Solving
-2.25 + x = 2.263846285

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.263846285 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.263846285 + 2.25
x = 2.263846285 + 2.25

Combine like terms: 2.263846285 + 2.25 = 4.513846285
x = 4.513846285

Simplifying
x = 4.513846285


Subproblem 2
x + -2.25 = -2.263846285

Simplifying
x + -2.25 = -2.263846285

Reorder the terms:
-2.25 + x = -2.263846285

Solving
-2.25 + x = -2.263846285

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.263846285 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.263846285 + 2.25
x = -2.263846285 + 2.25

Combine like terms: -2.263846285 + 2.25 = -0.013846285
x = -0.013846285

Simplifying
x = -0.013846285


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.513846285, -0.013846285}

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