6x^2+26x+26=0

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


Simplifying
6x2 + 26x + 26 = 0

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

Solving
26 + 26x + 6x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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

Simplifying
13 + 13x + 3x2 = 0

Solving
13 + 13x + 3x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = -4.333333333 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = -4.333333333 + 4.694444446

Combine like terms: -4.333333333 + 4.694444446 = 0.361111113
4.694444446 + 4.333333333x + x2 = 0.361111113

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 0.361111113

Calculate the square root of the right side: 0.600925214

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 0.600925214 and -0.600925214.


Subproblem 1
x + 2.166666667 = 0.600925214

Simplifying
x + 2.166666667 = 0.600925214

Reorder the terms:
2.166666667 + x = 0.600925214

Solving
2.166666667 + x = 0.600925214

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = 0.600925214 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = 0.600925214 + -2.166666667
x = 0.600925214 + -2.166666667

Combine like terms: 0.600925214 + -2.166666667 = -1.565741453
x = -1.565741453

Simplifying
x = -1.565741453


Subproblem 2
x + 2.166666667 = -0.600925214

Simplifying
x + 2.166666667 = -0.600925214

Reorder the terms:
2.166666667 + x = -0.600925214

Solving
2.166666667 + x = -0.600925214

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = -0.600925214 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = -0.600925214 + -2.166666667
x = -0.600925214 + -2.166666667

Combine like terms: -0.600925214 + -2.166666667 = -2.767591881
x = -2.767591881

Simplifying
x = -2.767591881


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.565741453, -2.767591881}
Solution
x = {-1.565741453, -2.767591881}

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