14x(14x)-22x-12=0

Solution for 14x(14x)-22x-12=0 equation:

Simplifying
14x(14x) + -22x + -12 = 0

Remove parenthesis around (14x)
14x * 14x + -22x + -12 = 0

Reorder the terms for easier multiplication:
14 * 14x * x + -22x + -12 = 0

Multiply 14 * 14
196x * x + -22x + -12 = 0

Multiply x * x
196x2 + -22x + -12 = 0

Reorder the terms:
-12 + -22x + 196x2 = 0

Solving
-12 + -22x + 196x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -11x + 98x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -11x + 98x2)' equal to zero and attempt to solve:

Simplifying
-6 + -11x + 98x2 = 0

Solving
-6 + -11x + 98x2 = 0

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

Divide each side by '98'.
-0.0612244898 + -0.112244898x + x2 = 0

Move the constant term to the right:

Add '0.0612244898' to each side of the equation.
-0.0612244898 + -0.112244898x + 0.0612244898 + x2 = 0 + 0.0612244898

Reorder the terms:
-0.0612244898 + 0.0612244898 + -0.112244898x + x2 = 0 + 0.0612244898

Combine like terms: -0.0612244898 + 0.0612244898 = 0.0000000000
0.0000000000 + -0.112244898x + x2 = 0 + 0.0612244898
-0.112244898x + x2 = 0 + 0.0612244898

Combine like terms: 0 + 0.0612244898 = 0.0612244898
-0.112244898x + x2 = 0.0612244898

The x term is -0.112244898x.  Take half its coefficient (-0.056122449).
Square it (0.003149729282) and add it to both sides.

Add '0.003149729282' to each side of the equation.
-0.112244898x + 0.003149729282 + x2 = 0.0612244898 + 0.003149729282

Reorder the terms:
0.003149729282 + -0.112244898x + x2 = 0.0612244898 + 0.003149729282

Combine like terms: 0.0612244898 + 0.003149729282 = 0.064374219082
0.003149729282 + -0.112244898x + x2 = 0.064374219082

Factor a perfect square on the left side:
(x + -0.056122449)(x + -0.056122449) = 0.064374219082

Calculate the square root of the right side: 0.25372075

Break this problem into two subproblems by setting 
(x + -0.056122449) equal to 0.25372075 and -0.25372075.

Subproblem 1
x + -0.056122449 = 0.25372075

Simplifying
x + -0.056122449 = 0.25372075

Reorder the terms:
-0.056122449 + x = 0.25372075

Solving
-0.056122449 + x = 0.25372075

Solving for variable 'x'.

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

Add '0.056122449' to each side of the equation.
-0.056122449 + 0.056122449 + x = 0.25372075 + 0.056122449

Combine like terms: -0.056122449 + 0.056122449 = 0.000000000
0.000000000 + x = 0.25372075 + 0.056122449
x = 0.25372075 + 0.056122449

Combine like terms: 0.25372075 + 0.056122449 = 0.309843199
x = 0.309843199

Simplifying
x = 0.309843199

Subproblem 2
x + -0.056122449 = -0.25372075

Simplifying
x + -0.056122449 = -0.25372075

Reorder the terms:
-0.056122449 + x = -0.25372075

Solving
-0.056122449 + x = -0.25372075

Solving for variable 'x'.

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

Add '0.056122449' to each side of the equation.
-0.056122449 + 0.056122449 + x = -0.25372075 + 0.056122449

Combine like terms: -0.056122449 + 0.056122449 = 0.000000000
0.000000000 + x = -0.25372075 + 0.056122449
x = -0.25372075 + 0.056122449

Combine like terms: -0.25372075 + 0.056122449 = -0.197598301
x = -0.197598301

Simplifying
x = -0.197598301

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.309843199, -0.197598301}
Solution
x = {0.309843199, -0.197598301}