16x^2-6x-14=0

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Solution for 16x^2-6x-14=0 equation: 


Simplifying
16x2 + -6x + -14 = 0

Reorder the terms:
-14 + -6x + 16x2 = 0

Solving
-14 + -6x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -3x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -3x + 8x2)' equal to zero and attempt to solve:

Simplifying
-7 + -3x + 8x2 = 0

Solving
-7 + -3x + 8x2 = 0

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

Divide each side by '8'.
-0.875 + -0.375x + x2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -0.375x + 0.875 + x2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -0.375x + x2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -0.375x + x2 = 0 + 0.875
-0.375x + x2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-0.375x + x2 = 0.875

The x term is -0.375x.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375x + 0.03515625 + x2 = 0.875 + 0.03515625

Reorder the terms:
0.03515625 + -0.375x + x2 = 0.875 + 0.03515625

Combine like terms: 0.875 + 0.03515625 = 0.91015625
0.03515625 + -0.375x + x2 = 0.91015625

Factor a perfect square on the left side:
(x + -0.1875)(x + -0.1875) = 0.91015625

Calculate the square root of the right side: 0.954021095

Break this problem into two subproblems by setting 
(x + -0.1875) equal to 0.954021095 and -0.954021095.


Subproblem 1
x + -0.1875 = 0.954021095

Simplifying
x + -0.1875 = 0.954021095

Reorder the terms:
-0.1875 + x = 0.954021095

Solving
-0.1875 + x = 0.954021095

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x = 0.954021095 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x = 0.954021095 + 0.1875
x = 0.954021095 + 0.1875

Combine like terms: 0.954021095 + 0.1875 = 1.141521095
x = 1.141521095

Simplifying
x = 1.141521095


Subproblem 2
x + -0.1875 = -0.954021095

Simplifying
x + -0.1875 = -0.954021095

Reorder the terms:
-0.1875 + x = -0.954021095

Solving
-0.1875 + x = -0.954021095

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x = -0.954021095 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x = -0.954021095 + 0.1875
x = -0.954021095 + 0.1875

Combine like terms: -0.954021095 + 0.1875 = -0.766521095
x = -0.766521095

Simplifying
x = -0.766521095


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.141521095, -0.766521095}
Solution
x = {1.141521095, -0.766521095}

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