6x^2+66x+26=0

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Solution for 6x^2+66x+26=0 equation: 


Simplifying
6x2 + 66x + 26 = 0

Reorder the terms:
26 + 66x + 6x2 = 0

Solving
26 + 66x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 33x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(13 + 33x + 3x2)' equal to zero and attempt to solve:

Simplifying
13 + 33x + 3x2 = 0

Solving
13 + 33x + 3x2 = 0

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

Divide each side by '3'.
4.333333333 + 11x + x2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + 11x + -4.333333333 + x2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + 11x + x2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + 11x + x2 = 0 + -4.333333333
11x + x2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
11x + x2 = -4.333333333

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -4.333333333 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -4.333333333 + 30.25

Combine like terms: -4.333333333 + 30.25 = 25.916666667
30.25 + 11x + x2 = 25.916666667

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 25.916666667

Calculate the square root of the right side: 5.09084145

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.09084145 and -5.09084145.


Subproblem 1
x + 5.5 = 5.09084145

Simplifying
x + 5.5 = 5.09084145

Reorder the terms:
5.5 + x = 5.09084145

Solving
5.5 + x = 5.09084145

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 5.09084145 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 5.09084145 + -5.5
x = 5.09084145 + -5.5

Combine like terms: 5.09084145 + -5.5 = -0.40915855
x = -0.40915855

Simplifying
x = -0.40915855


Subproblem 2
x + 5.5 = -5.09084145

Simplifying
x + 5.5 = -5.09084145

Reorder the terms:
5.5 + x = -5.09084145

Solving
5.5 + x = -5.09084145

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -5.09084145 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -5.09084145 + -5.5
x = -5.09084145 + -5.5

Combine like terms: -5.09084145 + -5.5 = -10.59084145
x = -10.59084145

Simplifying
x = -10.59084145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.40915855, -10.59084145}
Solution
x = {-0.40915855, -10.59084145}

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