14x^2+8x-2=0

Solution for 14x^2+8x-2=0 equation:

Simplifying
14x2 + 8x + -2 = 0

Reorder the terms:
-2 + 8x + 14x2 = 0

Solving
-2 + 8x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 4x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 4x + 7x2)' equal to zero and attempt to solve:

Simplifying
-1 + 4x + 7x2 = 0

Solving
-1 + 4x + 7x2 = 0

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

Divide each side by '7'.
-0.1428571429 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.5714285714x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 0.5714285714x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 0.5714285714x + x2 = 0 + 0.1428571429
0.5714285714x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
0.5714285714x + x2 = 0.1428571429

The x term is 0.5714285714x.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714x + 0.08163265305 + x2 = 0.1428571429 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 0.1428571429 + 0.08163265305

Combine like terms: 0.1428571429 + 0.08163265305 = 0.22448979595
0.08163265305 + 0.5714285714x + x2 = 0.22448979595

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 0.22448979595

Calculate the square root of the right side: 0.473803542

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 0.473803542 and -0.473803542.

Subproblem 1
x + 0.2857142857 = 0.473803542

Simplifying
x + 0.2857142857 = 0.473803542

Reorder the terms:
0.2857142857 + x = 0.473803542

Solving
0.2857142857 + x = 0.473803542

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = 0.473803542 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = 0.473803542 + -0.2857142857
x = 0.473803542 + -0.2857142857

Combine like terms: 0.473803542 + -0.2857142857 = 0.1880892563
x = 0.1880892563

Simplifying
x = 0.1880892563

Subproblem 2
x + 0.2857142857 = -0.473803542

Simplifying
x + 0.2857142857 = -0.473803542

Reorder the terms:
0.2857142857 + x = -0.473803542

Solving
0.2857142857 + x = -0.473803542

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = -0.473803542 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = -0.473803542 + -0.2857142857
x = -0.473803542 + -0.2857142857

Combine like terms: -0.473803542 + -0.2857142857 = -0.7595178277
x = -0.7595178277

Simplifying
x = -0.7595178277

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1880892563, -0.7595178277}
Solution
x = {0.1880892563, -0.7595178277}