6x^2-100x-36=0

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Solution for 6x^2-100x-36=0 equation: 


Simplifying
6x2 + -100x + -36 = 0

Reorder the terms:
-36 + -100x + 6x2 = 0

Solving
-36 + -100x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -50x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-18 + -50x + 3x2)' equal to zero and attempt to solve:

Simplifying
-18 + -50x + 3x2 = 0

Solving
-18 + -50x + 3x2 = 0

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

Divide each side by '3'.
-6 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -16.66666667x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -16.66666667x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -16.66666667x + x2 = 0 + 6
-16.66666667x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-16.66666667x + x2 = 6

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 = 6 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = 6 + 69.44444447

Combine like terms: 6 + 69.44444447 = 75.44444447
69.44444447 + -16.66666667x + x2 = 75.44444447

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 75.44444447

Calculate the square root of the right side: 8.685876149

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 8.685876149 and -8.685876149.


Subproblem 1
x + -8.333333335 = 8.685876149

Simplifying
x + -8.333333335 = 8.685876149

Reorder the terms:
-8.333333335 + x = 8.685876149

Solving
-8.333333335 + x = 8.685876149

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 = 8.685876149 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 8.685876149 + 8.333333335
x = 8.685876149 + 8.333333335

Combine like terms: 8.685876149 + 8.333333335 = 17.019209484
x = 17.019209484

Simplifying
x = 17.019209484


Subproblem 2
x + -8.333333335 = -8.685876149

Simplifying
x + -8.333333335 = -8.685876149

Reorder the terms:
-8.333333335 + x = -8.685876149

Solving
-8.333333335 + x = -8.685876149

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 = -8.685876149 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -8.685876149 + 8.333333335
x = -8.685876149 + 8.333333335

Combine like terms: -8.685876149 + 8.333333335 = -0.352542814
x = -0.352542814

Simplifying
x = -0.352542814


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.019209484, -0.352542814}
Solution
x = {17.019209484, -0.352542814}

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