x^2+36x-14580=0

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Solution for x^2+36x-14580=0 equation: 


Simplifying
x2 + 36x + -14580 = 0

Reorder the terms:
-14580 + 36x + x2 = 0

Solving
-14580 + 36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '14580' to each side of the equation.
-14580 + 36x + 14580 + x2 = 0 + 14580

Reorder the terms:
-14580 + 14580 + 36x + x2 = 0 + 14580

Combine like terms: -14580 + 14580 = 0
0 + 36x + x2 = 0 + 14580
36x + x2 = 0 + 14580

Combine like terms: 0 + 14580 = 14580
36x + x2 = 14580

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = 14580 + 324

Reorder the terms:
324 + 36x + x2 = 14580 + 324

Combine like terms: 14580 + 324 = 14904
324 + 36x + x2 = 14904

Factor a perfect square on the left side:
(x + 18)(x + 18) = 14904

Calculate the square root of the right side: 122.081939696

Break this problem into two subproblems by setting 
(x + 18) equal to 122.081939696 and -122.081939696.


Subproblem 1
x + 18 = 122.081939696

Simplifying
x + 18 = 122.081939696

Reorder the terms:
18 + x = 122.081939696

Solving
18 + x = 122.081939696

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = 122.081939696 + -18

Combine like terms: 18 + -18 = 0
0 + x = 122.081939696 + -18
x = 122.081939696 + -18

Combine like terms: 122.081939696 + -18 = 104.081939696
x = 104.081939696

Simplifying
x = 104.081939696


Subproblem 2
x + 18 = -122.081939696

Simplifying
x + 18 = -122.081939696

Reorder the terms:
18 + x = -122.081939696

Solving
18 + x = -122.081939696

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = -122.081939696 + -18

Combine like terms: 18 + -18 = 0
0 + x = -122.081939696 + -18
x = -122.081939696 + -18

Combine like terms: -122.081939696 + -18 = -140.081939696
x = -140.081939696

Simplifying
x = -140.081939696


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {104.081939696, -140.081939696}

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