12x^2+124x+24=0

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Solution for 12x^2+124x+24=0 equation: 


Simplifying
12x2 + 124x + 24 = 0

Reorder the terms:
24 + 124x + 12x2 = 0

Solving
24 + 124x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 31x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(6 + 31x + 3x2)' equal to zero and attempt to solve:

Simplifying
6 + 31x + 3x2 = 0

Solving
6 + 31x + 3x2 = 0

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

Divide each side by '3'.
2 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 10.33333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 10.33333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 10.33333333x + x2 = 0 + -2
10.33333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
10.33333333x + x2 = -2

The x term is 10.33333333x.  Take half its coefficient (5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
10.33333333x + 26.69444443 + x2 = -2 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = -2 + 26.69444443

Combine like terms: -2 + 26.69444443 = 24.69444443
26.69444443 + 10.33333333x + x2 = 24.69444443

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 24.69444443

Calculate the square root of the right side: 4.969350504

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 4.969350504 and -4.969350504.


Subproblem 1
x + 5.166666665 = 4.969350504

Simplifying
x + 5.166666665 = 4.969350504

Reorder the terms:
5.166666665 + x = 4.969350504

Solving
5.166666665 + x = 4.969350504

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = 4.969350504 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = 4.969350504 + -5.166666665
x = 4.969350504 + -5.166666665

Combine like terms: 4.969350504 + -5.166666665 = -0.197316161
x = -0.197316161

Simplifying
x = -0.197316161


Subproblem 2
x + 5.166666665 = -4.969350504

Simplifying
x + 5.166666665 = -4.969350504

Reorder the terms:
5.166666665 + x = -4.969350504

Solving
5.166666665 + x = -4.969350504

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = -4.969350504 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = -4.969350504 + -5.166666665
x = -4.969350504 + -5.166666665

Combine like terms: -4.969350504 + -5.166666665 = -10.136017169
x = -10.136017169

Simplifying
x = -10.136017169


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.197316161, -10.136017169}
Solution
x = {-0.197316161, -10.136017169}

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