8(x-8)-6x(x-5)+7x=

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Solution for 8(x-8)-6x(x-5)+7x= equation: 


Simplifying
8(x + -8) + -6x(x + -5) + 7x = 0

Reorder the terms:
8(-8 + x) + -6x(x + -5) + 7x = 0
(-8 * 8 + x * 8) + -6x(x + -5) + 7x = 0
(-64 + 8x) + -6x(x + -5) + 7x = 0

Reorder the terms:
-64 + 8x + -6x(-5 + x) + 7x = 0
-64 + 8x + (-5 * -6x + x * -6x) + 7x = 0
-64 + 8x + (30x + -6x2) + 7x = 0

Reorder the terms:
-64 + 8x + 30x + 7x + -6x2 = 0

Combine like terms: 8x + 30x = 38x
-64 + 38x + 7x + -6x2 = 0

Combine like terms: 38x + 7x = 45x
-64 + 45x + -6x2 = 0

Solving
-64 + 45x + -6x2 = 0

Solving for variable 'x'.

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

Divide each side by '-6'.
10.66666667 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-10.66666667' to each side of the equation.
10.66666667 + -7.5x + -10.66666667 + x2 = 0 + -10.66666667

Reorder the terms:
10.66666667 + -10.66666667 + -7.5x + x2 = 0 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + -7.5x + x2 = 0 + -10.66666667
-7.5x + x2 = 0 + -10.66666667

Combine like terms: 0 + -10.66666667 = -10.66666667
-7.5x + x2 = -10.66666667

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -10.66666667 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -10.66666667 + 14.0625

Combine like terms: -10.66666667 + 14.0625 = 3.39583333
14.0625 + -7.5x + x2 = 3.39583333

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 3.39583333

Calculate the square root of the right side: 1.842778698

Break this problem into two subproblems by setting 
(x + -3.75) equal to 1.842778698 and -1.842778698.


Subproblem 1
x + -3.75 = 1.842778698

Simplifying
x + -3.75 = 1.842778698

Reorder the terms:
-3.75 + x = 1.842778698

Solving
-3.75 + x = 1.842778698

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 1.842778698 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 1.842778698 + 3.75
x = 1.842778698 + 3.75

Combine like terms: 1.842778698 + 3.75 = 5.592778698
x = 5.592778698

Simplifying
x = 5.592778698


Subproblem 2
x + -3.75 = -1.842778698

Simplifying
x + -3.75 = -1.842778698

Reorder the terms:
-3.75 + x = -1.842778698

Solving
-3.75 + x = -1.842778698

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -1.842778698 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -1.842778698 + 3.75
x = -1.842778698 + 3.75

Combine like terms: -1.842778698 + 3.75 = 1.907221302
x = 1.907221302

Simplifying
x = 1.907221302


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.592778698, 1.907221302}

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