76-92x+6x^2=0

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Solution for 76-92x+6x^2=0 equation: 


Simplifying
76 + -92x + 6x2 = 0

Solving
76 + -92x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(38 + -46x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(38 + -46x + 3x2)' equal to zero and attempt to solve:

Simplifying
38 + -46x + 3x2 = 0

Solving
38 + -46x + 3x2 = 0

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

Divide each side by '3'.
12.66666667 + -15.33333333x + x2 = 0

Move the constant term to the right:

Add '-12.66666667' to each side of the equation.
12.66666667 + -15.33333333x + -12.66666667 + x2 = 0 + -12.66666667

Reorder the terms:
12.66666667 + -12.66666667 + -15.33333333x + x2 = 0 + -12.66666667

Combine like terms: 12.66666667 + -12.66666667 = 0.00000000
0.00000000 + -15.33333333x + x2 = 0 + -12.66666667
-15.33333333x + x2 = 0 + -12.66666667

Combine like terms: 0 + -12.66666667 = -12.66666667
-15.33333333x + x2 = -12.66666667

The x term is -15.33333333x.  Take half its coefficient (-7.666666665).
Square it (58.77777775) and add it to both sides.

Add '58.77777775' to each side of the equation.
-15.33333333x + 58.77777775 + x2 = -12.66666667 + 58.77777775

Reorder the terms:
58.77777775 + -15.33333333x + x2 = -12.66666667 + 58.77777775

Combine like terms: -12.66666667 + 58.77777775 = 46.11111108
58.77777775 + -15.33333333x + x2 = 46.11111108

Factor a perfect square on the left side:
(x + -7.666666665)(x + -7.666666665) = 46.11111108

Calculate the square root of the right side: 6.79051626

Break this problem into two subproblems by setting 
(x + -7.666666665) equal to 6.79051626 and -6.79051626.


Subproblem 1
x + -7.666666665 = 6.79051626

Simplifying
x + -7.666666665 = 6.79051626

Reorder the terms:
-7.666666665 + x = 6.79051626

Solving
-7.666666665 + x = 6.79051626

Solving for variable 'x'.

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

Add '7.666666665' to each side of the equation.
-7.666666665 + 7.666666665 + x = 6.79051626 + 7.666666665

Combine like terms: -7.666666665 + 7.666666665 = 0.000000000
0.000000000 + x = 6.79051626 + 7.666666665
x = 6.79051626 + 7.666666665

Combine like terms: 6.79051626 + 7.666666665 = 14.457182925
x = 14.457182925

Simplifying
x = 14.457182925


Subproblem 2
x + -7.666666665 = -6.79051626

Simplifying
x + -7.666666665 = -6.79051626

Reorder the terms:
-7.666666665 + x = -6.79051626

Solving
-7.666666665 + x = -6.79051626

Solving for variable 'x'.

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

Add '7.666666665' to each side of the equation.
-7.666666665 + 7.666666665 + x = -6.79051626 + 7.666666665

Combine like terms: -7.666666665 + 7.666666665 = 0.000000000
0.000000000 + x = -6.79051626 + 7.666666665
x = -6.79051626 + 7.666666665

Combine like terms: -6.79051626 + 7.666666665 = 0.876150405
x = 0.876150405

Simplifying
x = 0.876150405


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.457182925, 0.876150405}
Solution
x = {14.457182925, 0.876150405}

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