16x^2-20x-2=0

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Solution for 16x^2-20x-2=0 equation: 


Simplifying
16x2 + -20x + -2 = 0

Reorder the terms:
-2 + -20x + 16x2 = 0

Solving
-2 + -20x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -10x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -10x + 8x2)' equal to zero and attempt to solve:

Simplifying
-1 + -10x + 8x2 = 0

Solving
-1 + -10x + 8x2 = 0

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

Divide each side by '8'.
-0.125 + -1.25x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -1.25x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -1.25x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -1.25x + x2 = 0 + 0.125
-1.25x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-1.25x + x2 = 0.125

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 0.125 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 0.125 + 0.390625

Combine like terms: 0.125 + 0.390625 = 0.515625
0.390625 + -1.25x + x2 = 0.515625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(x + -0.625) equal to 0.718070331 and -0.718070331.


Subproblem 1
x + -0.625 = 0.718070331

Simplifying
x + -0.625 = 0.718070331

Reorder the terms:
-0.625 + x = 0.718070331

Solving
-0.625 + x = 0.718070331

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 0.718070331 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 0.718070331 + 0.625
x = 0.718070331 + 0.625

Combine like terms: 0.718070331 + 0.625 = 1.343070331
x = 1.343070331

Simplifying
x = 1.343070331


Subproblem 2
x + -0.625 = -0.718070331

Simplifying
x + -0.625 = -0.718070331

Reorder the terms:
-0.625 + x = -0.718070331

Solving
-0.625 + x = -0.718070331

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -0.718070331 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -0.718070331 + 0.625
x = -0.718070331 + 0.625

Combine like terms: -0.718070331 + 0.625 = -0.093070331
x = -0.093070331

Simplifying
x = -0.093070331


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.343070331, -0.093070331}
Solution
x = {1.343070331, -0.093070331}

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