2x^2+28x+6=0

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Solution for 2x^2+28x+6=0 equation: 


Simplifying
2x2 + 28x + 6 = 0

Reorder the terms:
6 + 28x + 2x2 = 0

Solving
6 + 28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
3 + 14x + x2 = 0

Solving
3 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 14x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 14x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 14x + x2 = 0 + -3
14x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
14x + x2 = -3

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -3 + 49

Reorder the terms:
49 + 14x + x2 = -3 + 49

Combine like terms: -3 + 49 = 46
49 + 14x + x2 = 46

Factor a perfect square on the left side:
(x + 7)(x + 7) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 7) equal to 6.782329983 and -6.782329983.


Subproblem 1
x + 7 = 6.782329983

Simplifying
x + 7 = 6.782329983

Reorder the terms:
7 + x = 6.782329983

Solving
7 + x = 6.782329983

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 6.782329983 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.782329983 + -7
x = 6.782329983 + -7

Combine like terms: 6.782329983 + -7 = -0.217670017
x = -0.217670017

Simplifying
x = -0.217670017


Subproblem 2
x + 7 = -6.782329983

Simplifying
x + 7 = -6.782329983

Reorder the terms:
7 + x = -6.782329983

Solving
7 + x = -6.782329983

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -6.782329983 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.782329983 + -7
x = -6.782329983 + -7

Combine like terms: -6.782329983 + -7 = -13.782329983
x = -13.782329983

Simplifying
x = -13.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.217670017, -13.782329983}
Solution
x = {-0.217670017, -13.782329983}

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