12x^2-280x+1200=0

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Solution for 12x^2-280x+1200=0 equation: 


Simplifying
12x2 + -280x + 1200 = 0

Reorder the terms:
1200 + -280x + 12x2 = 0

Solving
1200 + -280x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(300 + -70x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(300 + -70x + 3x2)' equal to zero and attempt to solve:

Simplifying
300 + -70x + 3x2 = 0

Solving
300 + -70x + 3x2 = 0

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

Divide each side by '3'.
100 + -23.33333333x + x2 = 0

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -23.33333333x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -23.33333333x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -23.33333333x + x2 = 0 + -100
-23.33333333x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-23.33333333x + x2 = -100

The x term is -23.33333333x.  Take half its coefficient (-11.66666667).
Square it (136.1111112) and add it to both sides.

Add '136.1111112' to each side of the equation.
-23.33333333x + 136.1111112 + x2 = -100 + 136.1111112

Reorder the terms:
136.1111112 + -23.33333333x + x2 = -100 + 136.1111112

Combine like terms: -100 + 136.1111112 = 36.1111112
136.1111112 + -23.33333333x + x2 = 36.1111112

Factor a perfect square on the left side:
(x + -11.66666667)(x + -11.66666667) = 36.1111112

Calculate the square root of the right side: 6.009252133

Break this problem into two subproblems by setting 
(x + -11.66666667) equal to 6.009252133 and -6.009252133.


Subproblem 1
x + -11.66666667 = 6.009252133

Simplifying
x + -11.66666667 = 6.009252133

Reorder the terms:
-11.66666667 + x = 6.009252133

Solving
-11.66666667 + x = 6.009252133

Solving for variable 'x'.

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

Add '11.66666667' to each side of the equation.
-11.66666667 + 11.66666667 + x = 6.009252133 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + x = 6.009252133 + 11.66666667
x = 6.009252133 + 11.66666667

Combine like terms: 6.009252133 + 11.66666667 = 17.675918803
x = 17.675918803

Simplifying
x = 17.675918803


Subproblem 2
x + -11.66666667 = -6.009252133

Simplifying
x + -11.66666667 = -6.009252133

Reorder the terms:
-11.66666667 + x = -6.009252133

Solving
-11.66666667 + x = -6.009252133

Solving for variable 'x'.

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

Add '11.66666667' to each side of the equation.
-11.66666667 + 11.66666667 + x = -6.009252133 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + x = -6.009252133 + 11.66666667
x = -6.009252133 + 11.66666667

Combine like terms: -6.009252133 + 11.66666667 = 5.657414537
x = 5.657414537

Simplifying
x = 5.657414537


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.675918803, 5.657414537}
Solution
x = {17.675918803, 5.657414537}

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