8x-(8x+x)=6x(x-8)+46

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Solution for 8x-(8x+x)=6x(x-8)+46 equation: 


Simplifying
8x + -1(8x + x) = 6x(x + -8) + 46

Combine like terms: 8x + x = 9x
8x + -1(9x) = 6x(x + -8) + 46

Remove parenthesis around (9x)
8x + -1 * 9x = 6x(x + -8) + 46

Multiply -1 * 9
8x + -9x = 6x(x + -8) + 46

Combine like terms: 8x + -9x = -1x
-1x = 6x(x + -8) + 46

Reorder the terms:
-1x = 6x(-8 + x) + 46
-1x = (-8 * 6x + x * 6x) + 46
-1x = (-48x + 6x2) + 46

Reorder the terms:
-1x = 46 + -48x + 6x2

Solving
-1x = 46 + -48x + 6x2

Solving for variable 'x'.

Reorder the terms:
-46 + -1x + 48x + -6x2 = 46 + -48x + 6x2 + -46 + 48x + -6x2

Combine like terms: -1x + 48x = 47x
-46 + 47x + -6x2 = 46 + -48x + 6x2 + -46 + 48x + -6x2

Reorder the terms:
-46 + 47x + -6x2 = 46 + -46 + -48x + 48x + 6x2 + -6x2

Combine like terms: 46 + -46 = 0
-46 + 47x + -6x2 = 0 + -48x + 48x + 6x2 + -6x2
-46 + 47x + -6x2 = -48x + 48x + 6x2 + -6x2

Combine like terms: -48x + 48x = 0
-46 + 47x + -6x2 = 0 + 6x2 + -6x2
-46 + 47x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-46 + 47x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
7.666666667 + -7.833333333x + x2 = 0

Move the constant term to the right:

Add '-7.666666667' to each side of the equation.
7.666666667 + -7.833333333x + -7.666666667 + x2 = 0 + -7.666666667

Reorder the terms:
7.666666667 + -7.666666667 + -7.833333333x + x2 = 0 + -7.666666667

Combine like terms: 7.666666667 + -7.666666667 = 0.000000000
0.000000000 + -7.833333333x + x2 = 0 + -7.666666667
-7.833333333x + x2 = 0 + -7.666666667

Combine like terms: 0 + -7.666666667 = -7.666666667
-7.833333333x + x2 = -7.666666667

The x term is -7.833333333x.  Take half its coefficient (-3.916666667).
Square it (15.34027778) and add it to both sides.

Add '15.34027778' to each side of the equation.
-7.833333333x + 15.34027778 + x2 = -7.666666667 + 15.34027778

Reorder the terms:
15.34027778 + -7.833333333x + x2 = -7.666666667 + 15.34027778

Combine like terms: -7.666666667 + 15.34027778 = 7.673611113
15.34027778 + -7.833333333x + x2 = 7.673611113

Factor a perfect square on the left side:
(x + -3.916666667)(x + -3.916666667) = 7.673611113

Calculate the square root of the right side: 2.770128357

Break this problem into two subproblems by setting 
(x + -3.916666667) equal to 2.770128357 and -2.770128357.


Subproblem 1
x + -3.916666667 = 2.770128357

Simplifying
x + -3.916666667 = 2.770128357

Reorder the terms:
-3.916666667 + x = 2.770128357

Solving
-3.916666667 + x = 2.770128357

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = 2.770128357 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = 2.770128357 + 3.916666667
x = 2.770128357 + 3.916666667

Combine like terms: 2.770128357 + 3.916666667 = 6.686795024
x = 6.686795024

Simplifying
x = 6.686795024


Subproblem 2
x + -3.916666667 = -2.770128357

Simplifying
x + -3.916666667 = -2.770128357

Reorder the terms:
-3.916666667 + x = -2.770128357

Solving
-3.916666667 + x = -2.770128357

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = -2.770128357 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = -2.770128357 + 3.916666667
x = -2.770128357 + 3.916666667

Combine like terms: -2.770128357 + 3.916666667 = 1.14653831
x = 1.14653831

Simplifying
x = 1.14653831


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.686795024, 1.14653831}

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