16x^2-112x-6=0

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Solution for 16x^2-112x-6=0 equation: 


Simplifying
16x2 + -112x + -6 = 0

Reorder the terms:
-6 + -112x + 16x2 = 0

Solving
-6 + -112x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -56x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -56x + 8x2)' equal to zero and attempt to solve:

Simplifying
-3 + -56x + 8x2 = 0

Solving
-3 + -56x + 8x2 = 0

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

Divide each side by '8'.
-0.375 + -7x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -7x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -7x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -7x + x2 = 0 + 0.375
-7x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-7x + x2 = 0.375

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 0.375 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 0.375 + 12.25

Combine like terms: 0.375 + 12.25 = 12.625
12.25 + -7x + x2 = 12.625

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 12.625

Calculate the square root of the right side: 3.553167601

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.553167601 and -3.553167601.


Subproblem 1
x + -3.5 = 3.553167601

Simplifying
x + -3.5 = 3.553167601

Reorder the terms:
-3.5 + x = 3.553167601

Solving
-3.5 + x = 3.553167601

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.553167601 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.553167601 + 3.5
x = 3.553167601 + 3.5

Combine like terms: 3.553167601 + 3.5 = 7.053167601
x = 7.053167601

Simplifying
x = 7.053167601


Subproblem 2
x + -3.5 = -3.553167601

Simplifying
x + -3.5 = -3.553167601

Reorder the terms:
-3.5 + x = -3.553167601

Solving
-3.5 + x = -3.553167601

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.553167601 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.553167601 + 3.5
x = -3.553167601 + 3.5

Combine like terms: -3.553167601 + 3.5 = -0.053167601
x = -0.053167601

Simplifying
x = -0.053167601


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.053167601, -0.053167601}
Solution
x = {7.053167601, -0.053167601}

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