8x-(4x-5)x=2

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Solution for 8x-(4x-5)x=2 equation: 


Simplifying
8x + -1(4x + -5) * x = 2

Reorder the terms:
8x + -1(-5 + 4x) * x = 2

Reorder the terms for easier multiplication:
8x + -1x(-5 + 4x) = 2
8x + (-5 * -1x + 4x * -1x) = 2
8x + (5x + -4x2) = 2

Combine like terms: 8x + 5x = 13x
13x + -4x2 = 2

Solving
13x + -4x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 13x + -4x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 13x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.5 + -3.25x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -3.25x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -3.25x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -3.25x + x2 = 0 + -0.5
-3.25x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-3.25x + x2 = -0.5

The x term is -3.25x.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25x + 2.640625 + x2 = -0.5 + 2.640625

Reorder the terms:
2.640625 + -3.25x + x2 = -0.5 + 2.640625

Combine like terms: -0.5 + 2.640625 = 2.140625
2.640625 + -3.25x + x2 = 2.140625

Factor a perfect square on the left side:
(x + -1.625)(x + -1.625) = 2.140625

Calculate the square root of the right side: 1.463087489

Break this problem into two subproblems by setting 
(x + -1.625) equal to 1.463087489 and -1.463087489.


Subproblem 1
x + -1.625 = 1.463087489

Simplifying
x + -1.625 = 1.463087489

Reorder the terms:
-1.625 + x = 1.463087489

Solving
-1.625 + x = 1.463087489

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = 1.463087489 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = 1.463087489 + 1.625
x = 1.463087489 + 1.625

Combine like terms: 1.463087489 + 1.625 = 3.088087489
x = 3.088087489

Simplifying
x = 3.088087489


Subproblem 2
x + -1.625 = -1.463087489

Simplifying
x + -1.625 = -1.463087489

Reorder the terms:
-1.625 + x = -1.463087489

Solving
-1.625 + x = -1.463087489

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = -1.463087489 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = -1.463087489 + 1.625
x = -1.463087489 + 1.625

Combine like terms: -1.463087489 + 1.625 = 0.161912511
x = 0.161912511

Simplifying
x = 0.161912511


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.088087489, 0.161912511}

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