6x^2-2x-100=0

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


Simplifying
6x2 + -2x + -100 = 0

Reorder the terms:
-100 + -2x + 6x2 = 0

Solving
-100 + -2x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -1x + 3x2) = 0

Ignore the factor 2.

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

Simplifying
-50 + -1x + 3x2 = 0

Solving
-50 + -1x + 3x2 = 0

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

Divide each side by '3'.
-16.66666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -0.3333333333x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -0.3333333333x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -0.3333333333x + x2 = 0 + 16.66666667
-0.3333333333x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-0.3333333333x + x2 = 16.66666667

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 16.66666667 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 16.66666667 + 0.02777777779

Combine like terms: 16.66666667 + 0.02777777779 = 16.69444444779
0.02777777779 + -0.3333333333x + x2 = 16.69444444779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 16.69444444779

Calculate the square root of the right side: 4.085883558

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 4.085883558 and -4.085883558.


Subproblem 1
x + -0.1666666667 = 4.085883558

Simplifying
x + -0.1666666667 = 4.085883558

Reorder the terms:
-0.1666666667 + x = 4.085883558

Solving
-0.1666666667 + x = 4.085883558

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 4.085883558 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 4.085883558 + 0.1666666667
x = 4.085883558 + 0.1666666667

Combine like terms: 4.085883558 + 0.1666666667 = 4.2525502247
x = 4.2525502247

Simplifying
x = 4.2525502247


Subproblem 2
x + -0.1666666667 = -4.085883558

Simplifying
x + -0.1666666667 = -4.085883558

Reorder the terms:
-0.1666666667 + x = -4.085883558

Solving
-0.1666666667 + x = -4.085883558

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -4.085883558 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -4.085883558 + 0.1666666667
x = -4.085883558 + 0.1666666667

Combine like terms: -4.085883558 + 0.1666666667 = -3.9192168913
x = -3.9192168913

Simplifying
x = -3.9192168913


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.2525502247, -3.9192168913}
Solution
x = {4.2525502247, -3.9192168913}

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