16x^2-28x-6=0

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Solution for 16x^2-28x-6=0 equation: 


Simplifying
16x2 + -28x + -6 = 0

Reorder the terms:
-6 + -28x + 16x2 = 0

Solving
-6 + -28x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -14x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -14x + 8x2)' equal to zero and attempt to solve:

Simplifying
-3 + -14x + 8x2 = 0

Solving
-3 + -14x + 8x2 = 0

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

Divide each side by '8'.
-0.375 + -1.75x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -1.75x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -1.75x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -1.75x + x2 = 0 + 0.375
-1.75x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-1.75x + x2 = 0.375

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 0.375 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 0.375 + 0.765625

Combine like terms: 0.375 + 0.765625 = 1.140625
0.765625 + -1.75x + x2 = 1.140625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.068000468 and -1.068000468.


Subproblem 1
x + -0.875 = 1.068000468

Simplifying
x + -0.875 = 1.068000468

Reorder the terms:
-0.875 + x = 1.068000468

Solving
-0.875 + x = 1.068000468

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 1.068000468 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 1.068000468 + 0.875
x = 1.068000468 + 0.875

Combine like terms: 1.068000468 + 0.875 = 1.943000468
x = 1.943000468

Simplifying
x = 1.943000468


Subproblem 2
x + -0.875 = -1.068000468

Simplifying
x + -0.875 = -1.068000468

Reorder the terms:
-0.875 + x = -1.068000468

Solving
-0.875 + x = -1.068000468

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -1.068000468 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -1.068000468 + 0.875
x = -1.068000468 + 0.875

Combine like terms: -1.068000468 + 0.875 = -0.193000468
x = -0.193000468

Simplifying
x = -0.193000468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.943000468, -0.193000468}
Solution
x = {1.943000468, -0.193000468}

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