16x^2-114x-14=0

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Solution for 16x^2-114x-14=0 equation: 


Simplifying
16x2 + -114x + -14 = 0

Reorder the terms:
-14 + -114x + 16x2 = 0

Solving
-14 + -114x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -57x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -57x + 8x2)' equal to zero and attempt to solve:

Simplifying
-7 + -57x + 8x2 = 0

Solving
-7 + -57x + 8x2 = 0

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

Divide each side by '8'.
-0.875 + -7.125x + x2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -7.125x + 0.875 + x2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -7.125x + x2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -7.125x + x2 = 0 + 0.875
-7.125x + x2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-7.125x + x2 = 0.875

The x term is -7.125x.  Take half its coefficient (-3.5625).
Square it (12.69140625) and add it to both sides.

Add '12.69140625' to each side of the equation.
-7.125x + 12.69140625 + x2 = 0.875 + 12.69140625

Reorder the terms:
12.69140625 + -7.125x + x2 = 0.875 + 12.69140625

Combine like terms: 0.875 + 12.69140625 = 13.56640625
12.69140625 + -7.125x + x2 = 13.56640625

Factor a perfect square on the left side:
(x + -3.5625)(x + -3.5625) = 13.56640625

Calculate the square root of the right side: 3.683260275

Break this problem into two subproblems by setting 
(x + -3.5625) equal to 3.683260275 and -3.683260275.


Subproblem 1
x + -3.5625 = 3.683260275

Simplifying
x + -3.5625 = 3.683260275

Reorder the terms:
-3.5625 + x = 3.683260275

Solving
-3.5625 + x = 3.683260275

Solving for variable 'x'.

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

Add '3.5625' to each side of the equation.
-3.5625 + 3.5625 + x = 3.683260275 + 3.5625

Combine like terms: -3.5625 + 3.5625 = 0.0000
0.0000 + x = 3.683260275 + 3.5625
x = 3.683260275 + 3.5625

Combine like terms: 3.683260275 + 3.5625 = 7.245760275
x = 7.245760275

Simplifying
x = 7.245760275


Subproblem 2
x + -3.5625 = -3.683260275

Simplifying
x + -3.5625 = -3.683260275

Reorder the terms:
-3.5625 + x = -3.683260275

Solving
-3.5625 + x = -3.683260275

Solving for variable 'x'.

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

Add '3.5625' to each side of the equation.
-3.5625 + 3.5625 + x = -3.683260275 + 3.5625

Combine like terms: -3.5625 + 3.5625 = 0.0000
0.0000 + x = -3.683260275 + 3.5625
x = -3.683260275 + 3.5625

Combine like terms: -3.683260275 + 3.5625 = -0.120760275
x = -0.120760275

Simplifying
x = -0.120760275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.245760275, -0.120760275}
Solution
x = {7.245760275, -0.120760275}

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