360x^2-12x-2550=0

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Solution for 360x^2-12x-2550=0 equation: 


Simplifying
360x2 + -12x + -2550 = 0

Reorder the terms:
-2550 + -12x + 360x2 = 0

Solving
-2550 + -12x + 360x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-425 + -2x + 60x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-425 + -2x + 60x2)' equal to zero and attempt to solve:

Simplifying
-425 + -2x + 60x2 = 0

Solving
-425 + -2x + 60x2 = 0

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

Divide each side by '60'.
-7.083333333 + -0.03333333333x + x2 = 0.0

Move the constant term to the right:

Add '7.083333333' to each side of the equation.
-7.083333333 + -0.03333333333x + 7.083333333 + x2 = 0.0 + 7.083333333

Reorder the terms:
-7.083333333 + 7.083333333 + -0.03333333333x + x2 = 0.0 + 7.083333333

Combine like terms: -7.083333333 + 7.083333333 = 0.000000000
0.000000000 + -0.03333333333x + x2 = 0.0 + 7.083333333
-0.03333333333x + x2 = 0.0 + 7.083333333

Combine like terms: 0.0 + 7.083333333 = 7.083333333
-0.03333333333x + x2 = 7.083333333

The x term is -0.03333333333x.  Take half its coefficient (-0.01666666667).
Square it (0.0002777777779) and add it to both sides.

Add '0.0002777777779' to each side of the equation.
-0.03333333333x + 0.0002777777779 + x2 = 7.083333333 + 0.0002777777779

Reorder the terms:
0.0002777777779 + -0.03333333333x + x2 = 7.083333333 + 0.0002777777779

Combine like terms: 7.083333333 + 0.0002777777779 = 7.0836111107779
0.0002777777779 + -0.03333333333x + x2 = 7.0836111107779

Factor a perfect square on the left side:
(x + -0.01666666667)(x + -0.01666666667) = 7.0836111107779

Calculate the square root of the right side: 2.661505422

Break this problem into two subproblems by setting 
(x + -0.01666666667) equal to 2.661505422 and -2.661505422.


Subproblem 1
x + -0.01666666667 = 2.661505422

Simplifying
x + -0.01666666667 = 2.661505422

Reorder the terms:
-0.01666666667 + x = 2.661505422

Solving
-0.01666666667 + x = 2.661505422

Solving for variable 'x'.

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

Add '0.01666666667' to each side of the equation.
-0.01666666667 + 0.01666666667 + x = 2.661505422 + 0.01666666667

Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000
0.00000000000 + x = 2.661505422 + 0.01666666667
x = 2.661505422 + 0.01666666667

Combine like terms: 2.661505422 + 0.01666666667 = 2.67817208867
x = 2.67817208867

Simplifying
x = 2.67817208867


Subproblem 2
x + -0.01666666667 = -2.661505422

Simplifying
x + -0.01666666667 = -2.661505422

Reorder the terms:
-0.01666666667 + x = -2.661505422

Solving
-0.01666666667 + x = -2.661505422

Solving for variable 'x'.

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

Add '0.01666666667' to each side of the equation.
-0.01666666667 + 0.01666666667 + x = -2.661505422 + 0.01666666667

Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000
0.00000000000 + x = -2.661505422 + 0.01666666667
x = -2.661505422 + 0.01666666667

Combine like terms: -2.661505422 + 0.01666666667 = -2.64483875533
x = -2.64483875533

Simplifying
x = -2.64483875533


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.67817208867, -2.64483875533}
Solution
x = {2.67817208867, -2.64483875533}

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