9x^2+120x+360=0

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Solution for 9x^2+120x+360=0 equation: 


Simplifying
9x2 + 120x + 360 = 0

Reorder the terms:
360 + 120x + 9x2 = 0

Solving
360 + 120x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(120 + 40x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(120 + 40x + 3x2)' equal to zero and attempt to solve:

Simplifying
120 + 40x + 3x2 = 0

Solving
120 + 40x + 3x2 = 0

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

Divide each side by '3'.
40 + 13.33333333x + x2 = 0

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 13.33333333x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 13.33333333x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 13.33333333x + x2 = 0 + -40
13.33333333x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
13.33333333x + x2 = -40

The x term is 13.33333333x.  Take half its coefficient (6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
13.33333333x + 44.44444442 + x2 = -40 + 44.44444442

Reorder the terms:
44.44444442 + 13.33333333x + x2 = -40 + 44.44444442

Combine like terms: -40 + 44.44444442 = 4.44444442
44.44444442 + 13.33333333x + x2 = 4.44444442

Factor a perfect square on the left side:
(x + 6.666666665)(x + 6.666666665) = 4.44444442

Calculate the square root of the right side: 2.108185101

Break this problem into two subproblems by setting 
(x + 6.666666665) equal to 2.108185101 and -2.108185101.


Subproblem 1
x + 6.666666665 = 2.108185101

Simplifying
x + 6.666666665 = 2.108185101

Reorder the terms:
6.666666665 + x = 2.108185101

Solving
6.666666665 + x = 2.108185101

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = 2.108185101 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = 2.108185101 + -6.666666665
x = 2.108185101 + -6.666666665

Combine like terms: 2.108185101 + -6.666666665 = -4.558481564
x = -4.558481564

Simplifying
x = -4.558481564


Subproblem 2
x + 6.666666665 = -2.108185101

Simplifying
x + 6.666666665 = -2.108185101

Reorder the terms:
6.666666665 + x = -2.108185101

Solving
6.666666665 + x = -2.108185101

Solving for variable 'x'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + x = -2.108185101 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + x = -2.108185101 + -6.666666665
x = -2.108185101 + -6.666666665

Combine like terms: -2.108185101 + -6.666666665 = -8.774851766
x = -8.774851766

Simplifying
x = -8.774851766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.558481564, -8.774851766}
Solution
x = {-4.558481564, -8.774851766}

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