36x^2-480x-2460=0

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Solution for 36x^2-480x-2460=0 equation: 


Simplifying
36x2 + -480x + -2460 = 0

Reorder the terms:
-2460 + -480x + 36x2 = 0

Solving
-2460 + -480x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-205 + -40x + 3x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-205 + -40x + 3x2)' equal to zero and attempt to solve:

Simplifying
-205 + -40x + 3x2 = 0

Solving
-205 + -40x + 3x2 = 0

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

Divide each side by '3'.
-68.33333333 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '68.33333333' to each side of the equation.
-68.33333333 + -13.33333333x + 68.33333333 + x2 = 0 + 68.33333333

Reorder the terms:
-68.33333333 + 68.33333333 + -13.33333333x + x2 = 0 + 68.33333333

Combine like terms: -68.33333333 + 68.33333333 = 0.00000000
0.00000000 + -13.33333333x + x2 = 0 + 68.33333333
-13.33333333x + x2 = 0 + 68.33333333

Combine like terms: 0 + 68.33333333 = 68.33333333
-13.33333333x + x2 = 68.33333333

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = 68.33333333 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = 68.33333333 + 44.44444442

Combine like terms: 68.33333333 + 44.44444442 = 112.77777775
44.44444442 + -13.33333333x + x2 = 112.77777775

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 112.77777775

Calculate the square root of the right side: 10.619688213

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 10.619688213 and -10.619688213.


Subproblem 1
x + -6.666666665 = 10.619688213

Simplifying
x + -6.666666665 = 10.619688213

Reorder the terms:
-6.666666665 + x = 10.619688213

Solving
-6.666666665 + x = 10.619688213

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 10.619688213 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 10.619688213 + 6.666666665
x = 10.619688213 + 6.666666665

Combine like terms: 10.619688213 + 6.666666665 = 17.286354878
x = 17.286354878

Simplifying
x = 17.286354878


Subproblem 2
x + -6.666666665 = -10.619688213

Simplifying
x + -6.666666665 = -10.619688213

Reorder the terms:
-6.666666665 + x = -10.619688213

Solving
-6.666666665 + x = -10.619688213

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -10.619688213 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -10.619688213 + 6.666666665
x = -10.619688213 + 6.666666665

Combine like terms: -10.619688213 + 6.666666665 = -3.953021548
x = -3.953021548

Simplifying
x = -3.953021548


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.286354878, -3.953021548}
Solution
x = {17.286354878, -3.953021548}

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