12x^2-240x-800=0

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Solution for 12x^2-240x-800=0 equation: 


Simplifying
12x2 + -240x + -800 = 0

Reorder the terms:
-800 + -240x + 12x2 = 0

Solving
-800 + -240x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-200 + -60x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-200 + -60x + 3x2)' equal to zero and attempt to solve:

Simplifying
-200 + -60x + 3x2 = 0

Solving
-200 + -60x + 3x2 = 0

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

Divide each side by '3'.
-66.66666667 + -20x + x2 = 0

Move the constant term to the right:

Add '66.66666667' to each side of the equation.
-66.66666667 + -20x + 66.66666667 + x2 = 0 + 66.66666667

Reorder the terms:
-66.66666667 + 66.66666667 + -20x + x2 = 0 + 66.66666667

Combine like terms: -66.66666667 + 66.66666667 = 0.00000000
0.00000000 + -20x + x2 = 0 + 66.66666667
-20x + x2 = 0 + 66.66666667

Combine like terms: 0 + 66.66666667 = 66.66666667
-20x + x2 = 66.66666667

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 = 66.66666667 + 100

Reorder the terms:
100 + -20x + x2 = 66.66666667 + 100

Combine like terms: 66.66666667 + 100 = 166.66666667
100 + -20x + x2 = 166.66666667

Factor a perfect square on the left side:
(x + -10)(x + -10) = 166.66666667

Calculate the square root of the right side: 12.909944487

Break this problem into two subproblems by setting 
(x + -10) equal to 12.909944487 and -12.909944487.


Subproblem 1
x + -10 = 12.909944487

Simplifying
x + -10 = 12.909944487

Reorder the terms:
-10 + x = 12.909944487

Solving
-10 + x = 12.909944487

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 = 12.909944487 + 10

Combine like terms: -10 + 10 = 0
0 + x = 12.909944487 + 10
x = 12.909944487 + 10

Combine like terms: 12.909944487 + 10 = 22.909944487
x = 22.909944487

Simplifying
x = 22.909944487


Subproblem 2
x + -10 = -12.909944487

Simplifying
x + -10 = -12.909944487

Reorder the terms:
-10 + x = -12.909944487

Solving
-10 + x = -12.909944487

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 = -12.909944487 + 10

Combine like terms: -10 + 10 = 0
0 + x = -12.909944487 + 10
x = -12.909944487 + 10

Combine like terms: -12.909944487 + 10 = -2.909944487
x = -2.909944487

Simplifying
x = -2.909944487


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.909944487, -2.909944487}
Solution
x = {22.909944487, -2.909944487}

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