12x^2-240x+819=

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Solution for 12x^2-240x+819= equation: 


Simplifying
12x2 + -240x + 819 = 0

Reorder the terms:
819 + -240x + 12x2 = 0

Solving
819 + -240x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(273 + -80x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(273 + -80x + 4x2)' equal to zero and attempt to solve:

Simplifying
273 + -80x + 4x2 = 0

Solving
273 + -80x + 4x2 = 0

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

Divide each side by '4'.
68.25 + -20x + x2 = 0

Move the constant term to the right:

Add '-68.25' to each side of the equation.
68.25 + -20x + -68.25 + x2 = 0 + -68.25

Reorder the terms:
68.25 + -68.25 + -20x + x2 = 0 + -68.25

Combine like terms: 68.25 + -68.25 = 0.00
0.00 + -20x + x2 = 0 + -68.25
-20x + x2 = 0 + -68.25

Combine like terms: 0 + -68.25 = -68.25
-20x + x2 = -68.25

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -68.25 + 100

Reorder the terms:
100 + -20x + x2 = -68.25 + 100

Combine like terms: -68.25 + 100 = 31.75
100 + -20x + x2 = 31.75

Factor a perfect square on the left side:
(x + -10)(x + -10) = 31.75

Calculate the square root of the right side: 5.634713835

Break this problem into two subproblems by setting 
(x + -10) equal to 5.634713835 and -5.634713835.


Subproblem 1
x + -10 = 5.634713835

Simplifying
x + -10 = 5.634713835

Reorder the terms:
-10 + x = 5.634713835

Solving
-10 + x = 5.634713835

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 5.634713835 + 10

Combine like terms: -10 + 10 = 0
0 + x = 5.634713835 + 10
x = 5.634713835 + 10

Combine like terms: 5.634713835 + 10 = 15.634713835
x = 15.634713835

Simplifying
x = 15.634713835


Subproblem 2
x + -10 = -5.634713835

Simplifying
x + -10 = -5.634713835

Reorder the terms:
-10 + x = -5.634713835

Solving
-10 + x = -5.634713835

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -5.634713835 + 10

Combine like terms: -10 + 10 = 0
0 + x = -5.634713835 + 10
x = -5.634713835 + 10

Combine like terms: -5.634713835 + 10 = 4.365286165
x = 4.365286165

Simplifying
x = 4.365286165


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.634713835, 4.365286165}
Solution
x = {15.634713835, 4.365286165}

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