14x^2-2x-4=0

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

Simplifying
14x2 + -2x + -4 = 0

Reorder the terms:
-4 + -2x + 14x2 = 0

Solving
-4 + -2x + 14x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-2 + -1x + 7x2 = 0

Solving
-2 + -1x + 7x2 = 0

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

Divide each side by '7'.
-0.2857142857 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -0.1428571429x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -0.1428571429x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -0.1428571429x + x2 = 0 + 0.2857142857
-0.1428571429x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-0.1428571429x + x2 = 0.2857142857

The x term is -0.1428571429x.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429x + 0.005102040819 + x2 = 0.2857142857 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 0.2857142857 + 0.005102040819

Combine like terms: 0.2857142857 + 0.005102040819 = 0.290816326519
0.005102040819 + -0.1428571429x + x2 = 0.290816326519

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 0.290816326519

Calculate the square root of the right side: 0.539273888

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 0.539273888 and -0.539273888.

Subproblem 1
x + -0.07142857145 = 0.539273888

Simplifying
x + -0.07142857145 = 0.539273888

Reorder the terms:
-0.07142857145 + x = 0.539273888

Solving
-0.07142857145 + x = 0.539273888

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = 0.539273888 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = 0.539273888 + 0.07142857145
x = 0.539273888 + 0.07142857145

Combine like terms: 0.539273888 + 0.07142857145 = 0.61070245945
x = 0.61070245945

Simplifying
x = 0.61070245945

Subproblem 2
x + -0.07142857145 = -0.539273888

Simplifying
x + -0.07142857145 = -0.539273888

Reorder the terms:
-0.07142857145 + x = -0.539273888

Solving
-0.07142857145 + x = -0.539273888

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = -0.539273888 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = -0.539273888 + 0.07142857145
x = -0.539273888 + 0.07142857145

Combine like terms: -0.539273888 + 0.07142857145 = -0.46784531655
x = -0.46784531655

Simplifying
x = -0.46784531655

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.61070245945, -0.46784531655}
Solution
x = {0.61070245945, -0.46784531655}