12x^2-120x+216=0

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Solution for 12x^2-120x+216=0 equation: 


Simplifying
12x2 + -120x + 216 = 0

Reorder the terms:
216 + -120x + 12x2 = 0

Solving
216 + -120x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(18 + -10x + x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(18 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
18 + -10x + x2 = 0

Solving
18 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -10x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -10x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -10x + x2 = 0 + -18
-10x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-10x + x2 = -18

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 = -18 + 25

Reorder the terms:
25 + -10x + x2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + -10x + x2 = 7

Factor a perfect square on the left side:
(x + -5)(x + -5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -5) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + -5 = 2.645751311

Simplifying
x + -5 = 2.645751311

Reorder the terms:
-5 + x = 2.645751311

Solving
-5 + x = 2.645751311

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 = 2.645751311 + 5

Combine like terms: -5 + 5 = 0
0 + x = 2.645751311 + 5
x = 2.645751311 + 5

Combine like terms: 2.645751311 + 5 = 7.645751311
x = 7.645751311

Simplifying
x = 7.645751311


Subproblem 2
x + -5 = -2.645751311

Simplifying
x + -5 = -2.645751311

Reorder the terms:
-5 + x = -2.645751311

Solving
-5 + x = -2.645751311

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 = -2.645751311 + 5

Combine like terms: -5 + 5 = 0
0 + x = -2.645751311 + 5
x = -2.645751311 + 5

Combine like terms: -2.645751311 + 5 = 2.354248689
x = 2.354248689

Simplifying
x = 2.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.645751311, 2.354248689}
Solution
x = {7.645751311, 2.354248689}

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