14x^2+28x+2=0

Solution for 14x^2+28x+2=0 equation:

Simplifying
14x2 + 28x + 2 = 0

Reorder the terms:
2 + 28x + 14x2 = 0

Solving
2 + 28x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 14x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 14x + 7x2)' equal to zero and attempt to solve:

Simplifying
1 + 14x + 7x2 = 0

Solving
1 + 14x + 7x2 = 0

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

Divide each side by '7'.
0.1428571429 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + 2x + -0.1428571429 + x2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + 2x + x2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + -0.1428571429
2x + x2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
2x + x2 = -0.1428571429

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.1428571429 + 1

Reorder the terms:
1 + 2x + x2 = -0.1428571429 + 1

Combine like terms: -0.1428571429 + 1 = 0.8571428571
1 + 2x + x2 = 0.8571428571

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.8571428571

Calculate the square root of the right side: 0.9258201

Break this problem into two subproblems by setting 
(x + 1) equal to 0.9258201 and -0.9258201.

Subproblem 1
x + 1 = 0.9258201

Simplifying
x + 1 = 0.9258201

Reorder the terms:
1 + x = 0.9258201

Solving
1 + x = 0.9258201

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 0.9258201 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.9258201 + -1
x = 0.9258201 + -1

Combine like terms: 0.9258201 + -1 = -0.0741799
x = -0.0741799

Simplifying
x = -0.0741799

Subproblem 2
x + 1 = -0.9258201

Simplifying
x + 1 = -0.9258201

Reorder the terms:
1 + x = -0.9258201

Solving
1 + x = -0.9258201

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -0.9258201 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.9258201 + -1
x = -0.9258201 + -1

Combine like terms: -0.9258201 + -1 = -1.9258201
x = -1.9258201

Simplifying
x = -1.9258201

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0741799, -1.9258201}
Solution
x = {-0.0741799, -1.9258201}