12x^2-136x+288=0

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Solution for 12x^2-136x+288=0 equation: 


Simplifying
12x2 + -136x + 288 = 0

Reorder the terms:
288 + -136x + 12x2 = 0

Solving
288 + -136x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(72 + -34x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(72 + -34x + 3x2)' equal to zero and attempt to solve:

Simplifying
72 + -34x + 3x2 = 0

Solving
72 + -34x + 3x2 = 0

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

Divide each side by '3'.
24 + -11.33333333x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -11.33333333x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -11.33333333x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -11.33333333x + x2 = 0 + -24
-11.33333333x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-11.33333333x + x2 = -24

The x term is -11.33333333x.  Take half its coefficient (-5.666666665).
Square it (32.11111109) and add it to both sides.

Add '32.11111109' to each side of the equation.
-11.33333333x + 32.11111109 + x2 = -24 + 32.11111109

Reorder the terms:
32.11111109 + -11.33333333x + x2 = -24 + 32.11111109

Combine like terms: -24 + 32.11111109 = 8.11111109
32.11111109 + -11.33333333x + x2 = 8.11111109

Factor a perfect square on the left side:
(x + -5.666666665)(x + -5.666666665) = 8.11111109

Calculate the square root of the right side: 2.848001245

Break this problem into two subproblems by setting 
(x + -5.666666665) equal to 2.848001245 and -2.848001245.


Subproblem 1
x + -5.666666665 = 2.848001245

Simplifying
x + -5.666666665 = 2.848001245

Reorder the terms:
-5.666666665 + x = 2.848001245

Solving
-5.666666665 + x = 2.848001245

Solving for variable 'x'.

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

Add '5.666666665' to each side of the equation.
-5.666666665 + 5.666666665 + x = 2.848001245 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = 2.848001245 + 5.666666665
x = 2.848001245 + 5.666666665

Combine like terms: 2.848001245 + 5.666666665 = 8.51466791
x = 8.51466791

Simplifying
x = 8.51466791


Subproblem 2
x + -5.666666665 = -2.848001245

Simplifying
x + -5.666666665 = -2.848001245

Reorder the terms:
-5.666666665 + x = -2.848001245

Solving
-5.666666665 + x = -2.848001245

Solving for variable 'x'.

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

Add '5.666666665' to each side of the equation.
-5.666666665 + 5.666666665 + x = -2.848001245 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + x = -2.848001245 + 5.666666665
x = -2.848001245 + 5.666666665

Combine like terms: -2.848001245 + 5.666666665 = 2.81866542
x = 2.81866542

Simplifying
x = 2.81866542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.51466791, 2.81866542}
Solution
x = {8.51466791, 2.81866542}

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