6x^2+68x-107=0

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Solution for 6x^2+68x-107=0 equation: 


Simplifying
6x2 + 68x + -107 = 0

Reorder the terms:
-107 + 68x + 6x2 = 0

Solving
-107 + 68x + 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'.
-17.83333333 + 11.33333333x + x2 = 0

Move the constant term to the right:

Add '17.83333333' to each side of the equation.
-17.83333333 + 11.33333333x + 17.83333333 + x2 = 0 + 17.83333333

Reorder the terms:
-17.83333333 + 17.83333333 + 11.33333333x + x2 = 0 + 17.83333333

Combine like terms: -17.83333333 + 17.83333333 = 0.00000000
0.00000000 + 11.33333333x + x2 = 0 + 17.83333333
11.33333333x + x2 = 0 + 17.83333333

Combine like terms: 0 + 17.83333333 = 17.83333333
11.33333333x + x2 = 17.83333333

The x term is 11.33333333x.  Take half its coefficient (5.666666665).
Square it (32.11111109) and add it to both sides.

Add '32.11111109' to each side of the equation.
11.33333333x + 32.11111109 + x2 = 17.83333333 + 32.11111109

Reorder the terms:
32.11111109 + 11.33333333x + x2 = 17.83333333 + 32.11111109

Combine like terms: 17.83333333 + 32.11111109 = 49.94444442
32.11111109 + 11.33333333x + x2 = 49.94444442

Factor a perfect square on the left side:
(x + 5.666666665)(x + 5.666666665) = 49.94444442

Calculate the square root of the right side: 7.067138347

Break this problem into two subproblems by setting 
(x + 5.666666665) equal to 7.067138347 and -7.067138347.


Subproblem 1
x + 5.666666665 = 7.067138347

Simplifying
x + 5.666666665 = 7.067138347

Reorder the terms:
5.666666665 + x = 7.067138347

Solving
5.666666665 + x = 7.067138347

Solving for variable 'x'.

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

Add '-5.666666665' to each side of the equation.
5.666666665 + -5.666666665 + x = 7.067138347 + -5.666666665

Combine like terms: 5.666666665 + -5.666666665 = 0.000000000
0.000000000 + x = 7.067138347 + -5.666666665
x = 7.067138347 + -5.666666665

Combine like terms: 7.067138347 + -5.666666665 = 1.400471682
x = 1.400471682

Simplifying
x = 1.400471682


Subproblem 2
x + 5.666666665 = -7.067138347

Simplifying
x + 5.666666665 = -7.067138347

Reorder the terms:
5.666666665 + x = -7.067138347

Solving
5.666666665 + x = -7.067138347

Solving for variable 'x'.

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

Add '-5.666666665' to each side of the equation.
5.666666665 + -5.666666665 + x = -7.067138347 + -5.666666665

Combine like terms: 5.666666665 + -5.666666665 = 0.000000000
0.000000000 + x = -7.067138347 + -5.666666665
x = -7.067138347 + -5.666666665

Combine like terms: -7.067138347 + -5.666666665 = -12.733805012
x = -12.733805012

Simplifying
x = -12.733805012


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.400471682, -12.733805012}

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