0=-16x^2-124x-6

Solution for 0=-16x^2-124x-6 equation:

Simplifying
0 = -16x2 + -124x + -6

Reorder the terms:
0 = -6 + -124x + -16x2

Solving
0 = -6 + -124x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + 124x + 16x2 = -6 + -124x + -16x2 + 6 + 124x + 16x2

Reorder the terms:
6 + 124x + 16x2 = -6 + 6 + -124x + 124x + -16x2 + 16x2

Combine like terms: -6 + 6 = 0
6 + 124x + 16x2 = 0 + -124x + 124x + -16x2 + 16x2
6 + 124x + 16x2 = -124x + 124x + -16x2 + 16x2

Combine like terms: -124x + 124x = 0
6 + 124x + 16x2 = 0 + -16x2 + 16x2
6 + 124x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
6 + 124x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 62x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 62x + 8x2)' equal to zero and attempt to solve:

Simplifying
3 + 62x + 8x2 = 0

Solving
3 + 62x + 8x2 = 0

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

Divide each side by '8'.
0.375 + 7.75x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 7.75x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 7.75x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 7.75x + x2 = 0 + -0.375
7.75x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
7.75x + x2 = -0.375

The x term is 7.75x.  Take half its coefficient (3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
7.75x + 15.015625 + x2 = -0.375 + 15.015625

Reorder the terms:
15.015625 + 7.75x + x2 = -0.375 + 15.015625

Combine like terms: -0.375 + 15.015625 = 14.640625
15.015625 + 7.75x + x2 = 14.640625

Factor a perfect square on the left side:
(x + 3.875)(x + 3.875) = 14.640625

Calculate the square root of the right side: 3.826306966

Break this problem into two subproblems by setting 
(x + 3.875) equal to 3.826306966 and -3.826306966.

Subproblem 1
x + 3.875 = 3.826306966

Simplifying
x + 3.875 = 3.826306966

Reorder the terms:
3.875 + x = 3.826306966

Solving
3.875 + x = 3.826306966

Solving for variable 'x'.

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

Add '-3.875' to each side of the equation.
3.875 + -3.875 + x = 3.826306966 + -3.875

Combine like terms: 3.875 + -3.875 = 0.000
0.000 + x = 3.826306966 + -3.875
x = 3.826306966 + -3.875

Combine like terms: 3.826306966 + -3.875 = -0.048693034
x = -0.048693034

Simplifying
x = -0.048693034

Subproblem 2
x + 3.875 = -3.826306966

Simplifying
x + 3.875 = -3.826306966

Reorder the terms:
3.875 + x = -3.826306966

Solving
3.875 + x = -3.826306966

Solving for variable 'x'.

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

Add '-3.875' to each side of the equation.
3.875 + -3.875 + x = -3.826306966 + -3.875

Combine like terms: 3.875 + -3.875 = 0.000
0.000 + x = -3.826306966 + -3.875
x = -3.826306966 + -3.875

Combine like terms: -3.826306966 + -3.875 = -7.701306966
x = -7.701306966

Simplifying
x = -7.701306966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.048693034, -7.701306966}
Solution
x = {-0.048693034, -7.701306966}