16x^2-100x-6=0

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Solution for 16x^2-100x-6=0 equation: 


Simplifying
16x2 + -100x + -6 = 0

Reorder the terms:
-6 + -100x + 16x2 = 0

Solving
-6 + -100x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -50x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -50x + 8x2)' equal to zero and attempt to solve:

Simplifying
-3 + -50x + 8x2 = 0

Solving
-3 + -50x + 8x2 = 0

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

Divide each side by '8'.
-0.375 + -6.25x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -6.25x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -6.25x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -6.25x + x2 = 0 + 0.375
-6.25x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-6.25x + x2 = 0.375

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = 0.375 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = 0.375 + 9.765625

Combine like terms: 0.375 + 9.765625 = 10.140625
9.765625 + -6.25x + x2 = 10.140625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 10.140625

Calculate the square root of the right side: 3.184434801

Break this problem into two subproblems by setting 
(x + -3.125) equal to 3.184434801 and -3.184434801.


Subproblem 1
x + -3.125 = 3.184434801

Simplifying
x + -3.125 = 3.184434801

Reorder the terms:
-3.125 + x = 3.184434801

Solving
-3.125 + x = 3.184434801

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 3.184434801 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 3.184434801 + 3.125
x = 3.184434801 + 3.125

Combine like terms: 3.184434801 + 3.125 = 6.309434801
x = 6.309434801

Simplifying
x = 6.309434801


Subproblem 2
x + -3.125 = -3.184434801

Simplifying
x + -3.125 = -3.184434801

Reorder the terms:
-3.125 + x = -3.184434801

Solving
-3.125 + x = -3.184434801

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -3.184434801 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -3.184434801 + 3.125
x = -3.184434801 + 3.125

Combine like terms: -3.184434801 + 3.125 = -0.059434801
x = -0.059434801

Simplifying
x = -0.059434801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.309434801, -0.059434801}
Solution
x = {6.309434801, -0.059434801}

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