12x^2+92x+96=0

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Solution for 12x^2+92x+96=0 equation: 


Simplifying
12x2 + 92x + 96 = 0

Reorder the terms:
96 + 92x + 12x2 = 0

Solving
96 + 92x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + 23x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(24 + 23x + 3x2)' equal to zero and attempt to solve:

Simplifying
24 + 23x + 3x2 = 0

Solving
24 + 23x + 3x2 = 0

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

Divide each side by '3'.
8 + 7.666666667x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 7.666666667x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 7.666666667x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7.666666667x + x2 = 0 + -8
7.666666667x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
7.666666667x + x2 = -8

The x term is 7.666666667x.  Take half its coefficient (3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
7.666666667x + 14.69444445 + x2 = -8 + 14.69444445

Reorder the terms:
14.69444445 + 7.666666667x + x2 = -8 + 14.69444445

Combine like terms: -8 + 14.69444445 = 6.69444445
14.69444445 + 7.666666667x + x2 = 6.69444445

Factor a perfect square on the left side:
(x + 3.833333334)(x + 3.833333334) = 6.69444445

Calculate the square root of the right side: 2.58736245

Break this problem into two subproblems by setting 
(x + 3.833333334) equal to 2.58736245 and -2.58736245.


Subproblem 1
x + 3.833333334 = 2.58736245

Simplifying
x + 3.833333334 = 2.58736245

Reorder the terms:
3.833333334 + x = 2.58736245

Solving
3.833333334 + x = 2.58736245

Solving for variable 'x'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + x = 2.58736245 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + x = 2.58736245 + -3.833333334
x = 2.58736245 + -3.833333334

Combine like terms: 2.58736245 + -3.833333334 = -1.245970884
x = -1.245970884

Simplifying
x = -1.245970884


Subproblem 2
x + 3.833333334 = -2.58736245

Simplifying
x + 3.833333334 = -2.58736245

Reorder the terms:
3.833333334 + x = -2.58736245

Solving
3.833333334 + x = -2.58736245

Solving for variable 'x'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + x = -2.58736245 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + x = -2.58736245 + -3.833333334
x = -2.58736245 + -3.833333334

Combine like terms: -2.58736245 + -3.833333334 = -6.420695784
x = -6.420695784

Simplifying
x = -6.420695784


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.245970884, -6.420695784}
Solution
x = {-1.245970884, -6.420695784}

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