-16x^2-120x-11=0

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Solution for -16x^2-120x-11=0 equation: 


Simplifying
-16x2 + -120x + -11 = 0

Reorder the terms:
-11 + -120x + -16x2 = 0

Solving
-11 + -120x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + 120x + 16x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(11 + 120x + 16x2)' equal to zero and attempt to solve:

Simplifying
11 + 120x + 16x2 = 0

Solving
11 + 120x + 16x2 = 0

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

Divide each side by '16'.
0.6875 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-0.6875' to each side of the equation.
0.6875 + 7.5x + -0.6875 + x2 = 0 + -0.6875

Reorder the terms:
0.6875 + -0.6875 + 7.5x + x2 = 0 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + 7.5x + x2 = 0 + -0.6875
7.5x + x2 = 0 + -0.6875

Combine like terms: 0 + -0.6875 = -0.6875
7.5x + x2 = -0.6875

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = -0.6875 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -0.6875 + 14.0625

Combine like terms: -0.6875 + 14.0625 = 13.375
14.0625 + 7.5x + x2 = 13.375

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 13.375

Calculate the square root of the right side: 3.65718471

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.65718471 and -3.65718471.


Subproblem 1
x + 3.75 = 3.65718471

Simplifying
x + 3.75 = 3.65718471

Reorder the terms:
3.75 + x = 3.65718471

Solving
3.75 + x = 3.65718471

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 3.65718471 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.65718471 + -3.75
x = 3.65718471 + -3.75

Combine like terms: 3.65718471 + -3.75 = -0.09281529
x = -0.09281529

Simplifying
x = -0.09281529


Subproblem 2
x + 3.75 = -3.65718471

Simplifying
x + 3.75 = -3.65718471

Reorder the terms:
3.75 + x = -3.65718471

Solving
3.75 + x = -3.65718471

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -3.65718471 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.65718471 + -3.75
x = -3.65718471 + -3.75

Combine like terms: -3.65718471 + -3.75 = -7.40718471
x = -7.40718471

Simplifying
x = -7.40718471


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.09281529, -7.40718471}
Solution
x = {-0.09281529, -7.40718471}

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