14x^2+14x-4=0

Solution for 14x^2+14x-4=0 equation:

Simplifying
14x2 + 14x + -4 = 0

Reorder the terms:
-4 + 14x + 14x2 = 0

Solving
-4 + 14x + 14x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-2 + 7x + 7x2 = 0

Solving
-2 + 7x + 7x2 = 0

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

Divide each side by '7'.
-0.2857142857 + x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x + x2 = 0 + 0.2857142857
x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
x + x2 = 0.2857142857

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.2857142857 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.2857142857 + 0.25

Combine like terms: 0.2857142857 + 0.25 = 0.5357142857
1.25 + x2 = 0.5357142857

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.5357142857

Calculate the square root of the right side: 0.731925055

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.731925055 and -0.731925055.

Subproblem 1
x + 0.5 = 0.731925055

Simplifying
x + 0.5 = 0.731925055

Reorder the terms:
0.5 + x = 0.731925055

Solving
0.5 + x = 0.731925055

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.731925055 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.731925055 + -0.5
x = 0.731925055 + -0.5

Combine like terms: 0.731925055 + -0.5 = 0.231925055
x = 0.231925055

Simplifying
x = 0.231925055

Subproblem 2
x + 0.5 = -0.731925055

Simplifying
x + 0.5 = -0.731925055

Reorder the terms:
0.5 + x = -0.731925055

Solving
0.5 + x = -0.731925055

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.731925055 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.731925055 + -0.5
x = -0.731925055 + -0.5

Combine like terms: -0.731925055 + -0.5 = -1.231925055
x = -1.231925055

Simplifying
x = -1.231925055

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.231925055, -1.231925055}
Solution
x = {0.231925055, -1.231925055}