6x^2-5x-136=0

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Solution for 6x^2-5x-136=0 equation: 


Simplifying
6x2 + -5x + -136 = 0

Reorder the terms:
-136 + -5x + 6x2 = 0

Solving
-136 + -5x + 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'.
-22.66666667 + -0.8333333333x + x2 = 0

Move the constant term to the right:

Add '22.66666667' to each side of the equation.
-22.66666667 + -0.8333333333x + 22.66666667 + x2 = 0 + 22.66666667

Reorder the terms:
-22.66666667 + 22.66666667 + -0.8333333333x + x2 = 0 + 22.66666667

Combine like terms: -22.66666667 + 22.66666667 = 0.00000000
0.00000000 + -0.8333333333x + x2 = 0 + 22.66666667
-0.8333333333x + x2 = 0 + 22.66666667

Combine like terms: 0 + 22.66666667 = 22.66666667
-0.8333333333x + x2 = 22.66666667

The x term is -0.8333333333x.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333x + 0.1736111111 + x2 = 22.66666667 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = 22.66666667 + 0.1736111111

Combine like terms: 22.66666667 + 0.1736111111 = 22.8402777811
0.1736111111 + -0.8333333333x + x2 = 22.8402777811

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 22.8402777811

Calculate the square root of the right side: 4.77915032

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 4.77915032 and -4.77915032.


Subproblem 1
x + -0.4166666667 = 4.77915032

Simplifying
x + -0.4166666667 = 4.77915032

Reorder the terms:
-0.4166666667 + x = 4.77915032

Solving
-0.4166666667 + x = 4.77915032

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = 4.77915032 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = 4.77915032 + 0.4166666667
x = 4.77915032 + 0.4166666667

Combine like terms: 4.77915032 + 0.4166666667 = 5.1958169867
x = 5.1958169867

Simplifying
x = 5.1958169867


Subproblem 2
x + -0.4166666667 = -4.77915032

Simplifying
x + -0.4166666667 = -4.77915032

Reorder the terms:
-0.4166666667 + x = -4.77915032

Solving
-0.4166666667 + x = -4.77915032

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = -4.77915032 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = -4.77915032 + 0.4166666667
x = -4.77915032 + 0.4166666667

Combine like terms: -4.77915032 + 0.4166666667 = -4.3624836533
x = -4.3624836533

Simplifying
x = -4.3624836533


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.1958169867, -4.3624836533}

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