0=36x^2-480x-2464

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Solution for 0=36x^2-480x-2464 equation: 


Simplifying
0 = 36x2 + -480x + -2464

Reorder the terms:
0 = -2464 + -480x + 36x2

Solving
0 = -2464 + -480x + 36x2

Solving for variable 'x'.

Combine like terms: 0 + 2464 = 2464
2464 + 480x + -36x2 = -2464 + -480x + 36x2 + 2464 + 480x + -36x2

Reorder the terms:
2464 + 480x + -36x2 = -2464 + 2464 + -480x + 480x + 36x2 + -36x2

Combine like terms: -2464 + 2464 = 0
2464 + 480x + -36x2 = 0 + -480x + 480x + 36x2 + -36x2
2464 + 480x + -36x2 = -480x + 480x + 36x2 + -36x2

Combine like terms: -480x + 480x = 0
2464 + 480x + -36x2 = 0 + 36x2 + -36x2
2464 + 480x + -36x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
2464 + 480x + -36x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(616 + 120x + -9x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(616 + 120x + -9x2)' equal to zero and attempt to solve:

Simplifying
616 + 120x + -9x2 = 0

Solving
616 + 120x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-68.44444444 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '68.44444444' to each side of the equation.
-68.44444444 + -13.33333333x + 68.44444444 + x2 = 0 + 68.44444444

Reorder the terms:
-68.44444444 + 68.44444444 + -13.33333333x + x2 = 0 + 68.44444444

Combine like terms: -68.44444444 + 68.44444444 = 0.00000000
0.00000000 + -13.33333333x + x2 = 0 + 68.44444444
-13.33333333x + x2 = 0 + 68.44444444

Combine like terms: 0 + 68.44444444 = 68.44444444
-13.33333333x + x2 = 68.44444444

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 = 68.44444444 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = 68.44444444 + 44.44444442

Combine like terms: 68.44444444 + 44.44444442 = 112.88888886
44.44444442 + -13.33333333x + x2 = 112.88888886

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 112.88888886

Calculate the square root of the right side: 10.624918299

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 10.624918299 and -10.624918299.


Subproblem 1
x + -6.666666665 = 10.624918299

Simplifying
x + -6.666666665 = 10.624918299

Reorder the terms:
-6.666666665 + x = 10.624918299

Solving
-6.666666665 + x = 10.624918299

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 = 10.624918299 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 10.624918299 + 6.666666665
x = 10.624918299 + 6.666666665

Combine like terms: 10.624918299 + 6.666666665 = 17.291584964
x = 17.291584964

Simplifying
x = 17.291584964


Subproblem 2
x + -6.666666665 = -10.624918299

Simplifying
x + -6.666666665 = -10.624918299

Reorder the terms:
-6.666666665 + x = -10.624918299

Solving
-6.666666665 + x = -10.624918299

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 = -10.624918299 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -10.624918299 + 6.666666665
x = -10.624918299 + 6.666666665

Combine like terms: -10.624918299 + 6.666666665 = -3.958251634
x = -3.958251634

Simplifying
x = -3.958251634


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.291584964, -3.958251634}
Solution
x = {17.291584964, -3.958251634}

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