32x^2-104x-2=0

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Solution for 32x^2-104x-2=0 equation: 


Simplifying
32x2 + -104x + -2 = 0

Reorder the terms:
-2 + -104x + 32x2 = 0

Solving
-2 + -104x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -52x + 16x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -52x + 16x2)' equal to zero and attempt to solve:

Simplifying
-1 + -52x + 16x2 = 0

Solving
-1 + -52x + 16x2 = 0

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

Divide each side by '16'.
-0.0625 + -3.25x + x2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + -3.25x + 0.0625 + x2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + -3.25x + x2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + -3.25x + x2 = 0 + 0.0625
-3.25x + x2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
-3.25x + x2 = 0.0625

The x term is -3.25x.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25x + 2.640625 + x2 = 0.0625 + 2.640625

Reorder the terms:
2.640625 + -3.25x + x2 = 0.0625 + 2.640625

Combine like terms: 0.0625 + 2.640625 = 2.703125
2.640625 + -3.25x + x2 = 2.703125

Factor a perfect square on the left side:
(x + -1.625)(x + -1.625) = 2.703125

Calculate the square root of the right side: 1.644118305

Break this problem into two subproblems by setting 
(x + -1.625) equal to 1.644118305 and -1.644118305.


Subproblem 1
x + -1.625 = 1.644118305

Simplifying
x + -1.625 = 1.644118305

Reorder the terms:
-1.625 + x = 1.644118305

Solving
-1.625 + x = 1.644118305

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = 1.644118305 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = 1.644118305 + 1.625
x = 1.644118305 + 1.625

Combine like terms: 1.644118305 + 1.625 = 3.269118305
x = 3.269118305

Simplifying
x = 3.269118305


Subproblem 2
x + -1.625 = -1.644118305

Simplifying
x + -1.625 = -1.644118305

Reorder the terms:
-1.625 + x = -1.644118305

Solving
-1.625 + x = -1.644118305

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = -1.644118305 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = -1.644118305 + 1.625
x = -1.644118305 + 1.625

Combine like terms: -1.644118305 + 1.625 = -0.019118305
x = -0.019118305

Simplifying
x = -0.019118305


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.269118305, -0.019118305}
Solution
x = {3.269118305, -0.019118305}

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