-16x^2-88x-48=0

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Solution for -16x^2-88x-48=0 equation: 


Simplifying
-16x2 + -88x + -48 = 0

Reorder the terms:
-48 + -88x + -16x2 = 0

Solving
-48 + -88x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-8'.
-8(6 + 11x + 2x2) = 0

Ignore the factor -8.

Subproblem 1
Set the factor '(6 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
6 + 11x + 2x2 = 0

Solving
6 + 11x + 2x2 = 0

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

Divide each side by '2'.
3 + 5.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 5.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5.5x + x2 = 0 + -3
5.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
5.5x + x2 = -3

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = -3 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -3 + 7.5625

Combine like terms: -3 + 7.5625 = 4.5625
7.5625 + 5.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + 2.75) equal to 2.136000936 and -2.136000936.


Subproblem 1
x + 2.75 = 2.136000936

Simplifying
x + 2.75 = 2.136000936

Reorder the terms:
2.75 + x = 2.136000936

Solving
2.75 + x = 2.136000936

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 2.136000936 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 2.136000936 + -2.75
x = 2.136000936 + -2.75

Combine like terms: 2.136000936 + -2.75 = -0.613999064
x = -0.613999064

Simplifying
x = -0.613999064


Subproblem 2
x + 2.75 = -2.136000936

Simplifying
x + 2.75 = -2.136000936

Reorder the terms:
2.75 + x = -2.136000936

Solving
2.75 + x = -2.136000936

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -2.136000936 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -2.136000936 + -2.75
x = -2.136000936 + -2.75

Combine like terms: -2.136000936 + -2.75 = -4.886000936
x = -4.886000936

Simplifying
x = -4.886000936


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.613999064, -4.886000936}
Solution
x = {-0.613999064, -4.886000936}

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