12x^2-120x+224=0

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Solution for 12x^2-120x+224=0 equation: 


Simplifying
12x2 + -120x + 224 = 0

Reorder the terms:
224 + -120x + 12x2 = 0

Solving
224 + -120x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(56 + -30x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(56 + -30x + 3x2)' equal to zero and attempt to solve:

Simplifying
56 + -30x + 3x2 = 0

Solving
56 + -30x + 3x2 = 0

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

Divide each side by '3'.
18.66666667 + -10x + x2 = 0

Move the constant term to the right:

Add '-18.66666667' to each side of the equation.
18.66666667 + -10x + -18.66666667 + x2 = 0 + -18.66666667

Reorder the terms:
18.66666667 + -18.66666667 + -10x + x2 = 0 + -18.66666667

Combine like terms: 18.66666667 + -18.66666667 = 0.00000000
0.00000000 + -10x + x2 = 0 + -18.66666667
-10x + x2 = 0 + -18.66666667

Combine like terms: 0 + -18.66666667 = -18.66666667
-10x + x2 = -18.66666667

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 = -18.66666667 + 25

Reorder the terms:
25 + -10x + x2 = -18.66666667 + 25

Combine like terms: -18.66666667 + 25 = 6.33333333
25 + -10x + x2 = 6.33333333

Factor a perfect square on the left side:
(x + -5)(x + -5) = 6.33333333

Calculate the square root of the right side: 2.516611478

Break this problem into two subproblems by setting 
(x + -5) equal to 2.516611478 and -2.516611478.


Subproblem 1
x + -5 = 2.516611478

Simplifying
x + -5 = 2.516611478

Reorder the terms:
-5 + x = 2.516611478

Solving
-5 + x = 2.516611478

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 = 2.516611478 + 5

Combine like terms: -5 + 5 = 0
0 + x = 2.516611478 + 5
x = 2.516611478 + 5

Combine like terms: 2.516611478 + 5 = 7.516611478
x = 7.516611478

Simplifying
x = 7.516611478


Subproblem 2
x + -5 = -2.516611478

Simplifying
x + -5 = -2.516611478

Reorder the terms:
-5 + x = -2.516611478

Solving
-5 + x = -2.516611478

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 = -2.516611478 + 5

Combine like terms: -5 + 5 = 0
0 + x = -2.516611478 + 5
x = -2.516611478 + 5

Combine like terms: -2.516611478 + 5 = 2.483388522
x = 2.483388522

Simplifying
x = 2.483388522


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.516611478, 2.483388522}
Solution
x = {7.516611478, 2.483388522}

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