36x^2-482x-2459=0

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Solution for 36x^2-482x-2459=0 equation: 


Simplifying
36x2 + -482x + -2459 = 0

Reorder the terms:
-2459 + -482x + 36x2 = 0

Solving
-2459 + -482x + 36x2 = 0

Solving for variable 'x'.

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

Divide each side by '36'.
-68.30555556 + -13.38888889x + x2 = 0

Move the constant term to the right:

Add '68.30555556' to each side of the equation.
-68.30555556 + -13.38888889x + 68.30555556 + x2 = 0 + 68.30555556

Reorder the terms:
-68.30555556 + 68.30555556 + -13.38888889x + x2 = 0 + 68.30555556

Combine like terms: -68.30555556 + 68.30555556 = 0.00000000
0.00000000 + -13.38888889x + x2 = 0 + 68.30555556
-13.38888889x + x2 = 0 + 68.30555556

Combine like terms: 0 + 68.30555556 = 68.30555556
-13.38888889x + x2 = 68.30555556

The x term is -13.38888889x.  Take half its coefficient (-6.694444445).
Square it (44.81558643) and add it to both sides.

Add '44.81558643' to each side of the equation.
-13.38888889x + 44.81558643 + x2 = 68.30555556 + 44.81558643

Reorder the terms:
44.81558643 + -13.38888889x + x2 = 68.30555556 + 44.81558643

Combine like terms: 68.30555556 + 44.81558643 = 113.12114199
44.81558643 + -13.38888889x + x2 = 113.12114199

Factor a perfect square on the left side:
(x + -6.694444445)(x + -6.694444445) = 113.12114199

Calculate the square root of the right side: 10.635842326

Break this problem into two subproblems by setting 
(x + -6.694444445) equal to 10.635842326 and -10.635842326.


Subproblem 1
x + -6.694444445 = 10.635842326

Simplifying
x + -6.694444445 = 10.635842326

Reorder the terms:
-6.694444445 + x = 10.635842326

Solving
-6.694444445 + x = 10.635842326

Solving for variable 'x'.

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

Add '6.694444445' to each side of the equation.
-6.694444445 + 6.694444445 + x = 10.635842326 + 6.694444445

Combine like terms: -6.694444445 + 6.694444445 = 0.000000000
0.000000000 + x = 10.635842326 + 6.694444445
x = 10.635842326 + 6.694444445

Combine like terms: 10.635842326 + 6.694444445 = 17.330286771
x = 17.330286771

Simplifying
x = 17.330286771


Subproblem 2
x + -6.694444445 = -10.635842326

Simplifying
x + -6.694444445 = -10.635842326

Reorder the terms:
-6.694444445 + x = -10.635842326

Solving
-6.694444445 + x = -10.635842326

Solving for variable 'x'.

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

Add '6.694444445' to each side of the equation.
-6.694444445 + 6.694444445 + x = -10.635842326 + 6.694444445

Combine like terms: -6.694444445 + 6.694444445 = 0.000000000
0.000000000 + x = -10.635842326 + 6.694444445
x = -10.635842326 + 6.694444445

Combine like terms: -10.635842326 + 6.694444445 = -3.941397881
x = -3.941397881

Simplifying
x = -3.941397881


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.330286771, -3.941397881}

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