6x^2+6x-2200=0

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Solution for 6x^2+6x-2200=0 equation: 


Simplifying
6x2 + 6x + -2200 = 0

Reorder the terms:
-2200 + 6x + 6x2 = 0

Solving
-2200 + 6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1100 + 3x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1100 + 3x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1100 + 3x + 3x2 = 0

Solving
-1100 + 3x + 3x2 = 0

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

Divide each side by '3'.
-366.6666667 + x + x2 = 0

Move the constant term to the right:

Add '366.6666667' to each side of the equation.
-366.6666667 + x + 366.6666667 + x2 = 0 + 366.6666667

Reorder the terms:
-366.6666667 + 366.6666667 + x + x2 = 0 + 366.6666667

Combine like terms: -366.6666667 + 366.6666667 = 0.0000000
0.0000000 + x + x2 = 0 + 366.6666667
x + x2 = 0 + 366.6666667

Combine like terms: 0 + 366.6666667 = 366.6666667
x + x2 = 366.6666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 366.6666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 366.6666667 + 0.25

Combine like terms: 366.6666667 + 0.25 = 366.9166667
1.25 + x2 = 366.9166667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 366.9166667

Calculate the square root of the right side: 19.155068956

Break this problem into two subproblems by setting 
(x + 0.5) equal to 19.155068956 and -19.155068956.


Subproblem 1
x + 0.5 = 19.155068956

Simplifying
x + 0.5 = 19.155068956

Reorder the terms:
0.5 + x = 19.155068956

Solving
0.5 + x = 19.155068956

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 19.155068956 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 19.155068956 + -0.5
x = 19.155068956 + -0.5

Combine like terms: 19.155068956 + -0.5 = 18.655068956
x = 18.655068956

Simplifying
x = 18.655068956


Subproblem 2
x + 0.5 = -19.155068956

Simplifying
x + 0.5 = -19.155068956

Reorder the terms:
0.5 + x = -19.155068956

Solving
0.5 + x = -19.155068956

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -19.155068956 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -19.155068956 + -0.5
x = -19.155068956 + -0.5

Combine like terms: -19.155068956 + -0.5 = -19.655068956
x = -19.655068956

Simplifying
x = -19.655068956


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.655068956, -19.655068956}
Solution
x = {18.655068956, -19.655068956}

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