12x^2-228x+741=0

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Solution for 12x^2-228x+741=0 equation: 


Simplifying
12x2 + -228x + 741 = 0

Reorder the terms:
741 + -228x + 12x2 = 0

Solving
741 + -228x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(247 + -76x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(247 + -76x + 4x2)' equal to zero and attempt to solve:

Simplifying
247 + -76x + 4x2 = 0

Solving
247 + -76x + 4x2 = 0

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

Divide each side by '4'.
61.75 + -19x + x2 = 0

Move the constant term to the right:

Add '-61.75' to each side of the equation.
61.75 + -19x + -61.75 + x2 = 0 + -61.75

Reorder the terms:
61.75 + -61.75 + -19x + x2 = 0 + -61.75

Combine like terms: 61.75 + -61.75 = 0.00
0.00 + -19x + x2 = 0 + -61.75
-19x + x2 = 0 + -61.75

Combine like terms: 0 + -61.75 = -61.75
-19x + x2 = -61.75

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = -61.75 + 90.25

Reorder the terms:
90.25 + -19x + x2 = -61.75 + 90.25

Combine like terms: -61.75 + 90.25 = 28.5
90.25 + -19x + x2 = 28.5

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 28.5

Calculate the square root of the right side: 5.338539126

Break this problem into two subproblems by setting 
(x + -9.5) equal to 5.338539126 and -5.338539126.


Subproblem 1
x + -9.5 = 5.338539126

Simplifying
x + -9.5 = 5.338539126

Reorder the terms:
-9.5 + x = 5.338539126

Solving
-9.5 + x = 5.338539126

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 5.338539126 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 5.338539126 + 9.5
x = 5.338539126 + 9.5

Combine like terms: 5.338539126 + 9.5 = 14.838539126
x = 14.838539126

Simplifying
x = 14.838539126


Subproblem 2
x + -9.5 = -5.338539126

Simplifying
x + -9.5 = -5.338539126

Reorder the terms:
-9.5 + x = -5.338539126

Solving
-9.5 + x = -5.338539126

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -5.338539126 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -5.338539126 + 9.5
x = -5.338539126 + 9.5

Combine like terms: -5.338539126 + 9.5 = 4.161460874
x = 4.161460874

Simplifying
x = 4.161460874


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.838539126, 4.161460874}
Solution
x = {14.838539126, 4.161460874}

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