6x^2+78x+26=0

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Solution for 6x^2+78x+26=0 equation: 


Simplifying
6x2 + 78x + 26 = 0

Reorder the terms:
26 + 78x + 6x2 = 0

Solving
26 + 78x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 39x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(13 + 39x + 3x2)' equal to zero and attempt to solve:

Simplifying
13 + 39x + 3x2 = 0

Solving
13 + 39x + 3x2 = 0

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

Divide each side by '3'.
4.333333333 + 13x + x2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + 13x + -4.333333333 + x2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + 13x + x2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + 13x + x2 = 0 + -4.333333333
13x + x2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
13x + x2 = -4.333333333

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = -4.333333333 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -4.333333333 + 42.25

Combine like terms: -4.333333333 + 42.25 = 37.916666667
42.25 + 13x + x2 = 37.916666667

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 37.916666667

Calculate the square root of the right side: 6.157651067

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.157651067 and -6.157651067.


Subproblem 1
x + 6.5 = 6.157651067

Simplifying
x + 6.5 = 6.157651067

Reorder the terms:
6.5 + x = 6.157651067

Solving
6.5 + x = 6.157651067

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 6.157651067 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.157651067 + -6.5
x = 6.157651067 + -6.5

Combine like terms: 6.157651067 + -6.5 = -0.342348933
x = -0.342348933

Simplifying
x = -0.342348933


Subproblem 2
x + 6.5 = -6.157651067

Simplifying
x + 6.5 = -6.157651067

Reorder the terms:
6.5 + x = -6.157651067

Solving
6.5 + x = -6.157651067

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -6.157651067 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.157651067 + -6.5
x = -6.157651067 + -6.5

Combine like terms: -6.157651067 + -6.5 = -12.657651067
x = -12.657651067

Simplifying
x = -12.657651067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.342348933, -12.657651067}
Solution
x = {-0.342348933, -12.657651067}

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