6x^2+42x+26=0

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Solution for 6x^2+42x+26=0 equation: 


Simplifying
6x2 + 42x + 26 = 0

Reorder the terms:
26 + 42x + 6x2 = 0

Solving
26 + 42x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 21x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(13 + 21x + 3x2)' equal to zero and attempt to solve:

Simplifying
13 + 21x + 3x2 = 0

Solving
13 + 21x + 3x2 = 0

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

Divide each side by '3'.
4.333333333 + 7x + x2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + 7x + -4.333333333 + x2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + 7x + x2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + 7x + x2 = 0 + -4.333333333
7x + x2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
7x + x2 = -4.333333333

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -4.333333333 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -4.333333333 + 12.25

Combine like terms: -4.333333333 + 12.25 = 7.916666667
12.25 + 7x + x2 = 7.916666667

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 7.916666667

Calculate the square root of the right side: 2.813657169

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.813657169 and -2.813657169.


Subproblem 1
x + 3.5 = 2.813657169

Simplifying
x + 3.5 = 2.813657169

Reorder the terms:
3.5 + x = 2.813657169

Solving
3.5 + x = 2.813657169

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 2.813657169 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 2.813657169 + -3.5
x = 2.813657169 + -3.5

Combine like terms: 2.813657169 + -3.5 = -0.686342831
x = -0.686342831

Simplifying
x = -0.686342831


Subproblem 2
x + 3.5 = -2.813657169

Simplifying
x + 3.5 = -2.813657169

Reorder the terms:
3.5 + x = -2.813657169

Solving
3.5 + x = -2.813657169

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -2.813657169 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -2.813657169 + -3.5
x = -2.813657169 + -3.5

Combine like terms: -2.813657169 + -3.5 = -6.313657169
x = -6.313657169

Simplifying
x = -6.313657169


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.686342831, -6.313657169}
Solution
x = {-0.686342831, -6.313657169}

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