12x^2+120x+176=0

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Solution for 12x^2+120x+176=0 equation: 


Simplifying
12x2 + 120x + 176 = 0

Reorder the terms:
176 + 120x + 12x2 = 0

Solving
176 + 120x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(44 + 30x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(44 + 30x + 3x2)' equal to zero and attempt to solve:

Simplifying
44 + 30x + 3x2 = 0

Solving
44 + 30x + 3x2 = 0

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

Divide each side by '3'.
14.66666667 + 10x + x2 = 0

Move the constant term to the right:

Add '-14.66666667' to each side of the equation.
14.66666667 + 10x + -14.66666667 + x2 = 0 + -14.66666667

Reorder the terms:
14.66666667 + -14.66666667 + 10x + x2 = 0 + -14.66666667

Combine like terms: 14.66666667 + -14.66666667 = 0.00000000
0.00000000 + 10x + x2 = 0 + -14.66666667
10x + x2 = 0 + -14.66666667

Combine like terms: 0 + -14.66666667 = -14.66666667
10x + x2 = -14.66666667

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -14.66666667 + 25

Reorder the terms:
25 + 10x + x2 = -14.66666667 + 25

Combine like terms: -14.66666667 + 25 = 10.33333333
25 + 10x + x2 = 10.33333333

Factor a perfect square on the left side:
(x + 5)(x + 5) = 10.33333333

Calculate the square root of the right side: 3.214550253

Break this problem into two subproblems by setting 
(x + 5) equal to 3.214550253 and -3.214550253.


Subproblem 1
x + 5 = 3.214550253

Simplifying
x + 5 = 3.214550253

Reorder the terms:
5 + x = 3.214550253

Solving
5 + x = 3.214550253

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 3.214550253 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.214550253 + -5
x = 3.214550253 + -5

Combine like terms: 3.214550253 + -5 = -1.785449747
x = -1.785449747

Simplifying
x = -1.785449747


Subproblem 2
x + 5 = -3.214550253

Simplifying
x + 5 = -3.214550253

Reorder the terms:
5 + x = -3.214550253

Solving
5 + x = -3.214550253

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -3.214550253 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.214550253 + -5
x = -3.214550253 + -5

Combine like terms: -3.214550253 + -5 = -8.214550253
x = -8.214550253

Simplifying
x = -8.214550253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.785449747, -8.214550253}
Solution
x = {-1.785449747, -8.214550253}

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