6x^2-100x-100=0

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Solution for 6x^2-100x-100=0 equation: 


Simplifying
6x2 + -100x + -100 = 0

Reorder the terms:
-100 + -100x + 6x2 = 0

Solving
-100 + -100x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -50x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + -50x + 3x2)' equal to zero and attempt to solve:

Simplifying
-50 + -50x + 3x2 = 0

Solving
-50 + -50x + 3x2 = 0

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

Divide each side by '3'.
-16.66666667 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -16.66666667x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -16.66666667x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -16.66666667x + x2 = 0 + 16.66666667
-16.66666667x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-16.66666667x + x2 = 16.66666667

The x term is -16.66666667x.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667x + 69.44444447 + x2 = 16.66666667 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = 16.66666667 + 69.44444447

Combine like terms: 16.66666667 + 69.44444447 = 86.11111114
69.44444447 + -16.66666667x + x2 = 86.11111114

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 86.11111114

Calculate the square root of the right side: 9.279607273

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 9.279607273 and -9.279607273.


Subproblem 1
x + -8.333333335 = 9.279607273

Simplifying
x + -8.333333335 = 9.279607273

Reorder the terms:
-8.333333335 + x = 9.279607273

Solving
-8.333333335 + x = 9.279607273

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = 9.279607273 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 9.279607273 + 8.333333335
x = 9.279607273 + 8.333333335

Combine like terms: 9.279607273 + 8.333333335 = 17.612940608
x = 17.612940608

Simplifying
x = 17.612940608


Subproblem 2
x + -8.333333335 = -9.279607273

Simplifying
x + -8.333333335 = -9.279607273

Reorder the terms:
-8.333333335 + x = -9.279607273

Solving
-8.333333335 + x = -9.279607273

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = -9.279607273 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -9.279607273 + 8.333333335
x = -9.279607273 + 8.333333335

Combine like terms: -9.279607273 + 8.333333335 = -0.946273938
x = -0.946273938

Simplifying
x = -0.946273938


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.612940608, -0.946273938}
Solution
x = {17.612940608, -0.946273938}

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