-x^2-36x+2160=0

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Solution for -x^2-36x+2160=0 equation: 


Simplifying
-1x2 + -36x + 2160 = 0

Reorder the terms:
2160 + -36x + -1x2 = 0

Solving
2160 + -36x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2160 + 36x + x2 = 0

Move the constant term to the right:

Add '2160' to each side of the equation.
-2160 + 36x + 2160 + x2 = 0 + 2160

Reorder the terms:
-2160 + 2160 + 36x + x2 = 0 + 2160

Combine like terms: -2160 + 2160 = 0
0 + 36x + x2 = 0 + 2160
36x + x2 = 0 + 2160

Combine like terms: 0 + 2160 = 2160
36x + x2 = 2160

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 = 2160 + 324

Reorder the terms:
324 + 36x + x2 = 2160 + 324

Combine like terms: 2160 + 324 = 2484
324 + 36x + x2 = 2484

Factor a perfect square on the left side:
(x + 18)(x + 18) = 2484

Calculate the square root of the right side: 49.839743178

Break this problem into two subproblems by setting 
(x + 18) equal to 49.839743178 and -49.839743178.


Subproblem 1
x + 18 = 49.839743178

Simplifying
x + 18 = 49.839743178

Reorder the terms:
18 + x = 49.839743178

Solving
18 + x = 49.839743178

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 = 49.839743178 + -18

Combine like terms: 18 + -18 = 0
0 + x = 49.839743178 + -18
x = 49.839743178 + -18

Combine like terms: 49.839743178 + -18 = 31.839743178
x = 31.839743178

Simplifying
x = 31.839743178


Subproblem 2
x + 18 = -49.839743178

Simplifying
x + 18 = -49.839743178

Reorder the terms:
18 + x = -49.839743178

Solving
18 + x = -49.839743178

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 = -49.839743178 + -18

Combine like terms: 18 + -18 = 0
0 + x = -49.839743178 + -18
x = -49.839743178 + -18

Combine like terms: -49.839743178 + -18 = -67.839743178
x = -67.839743178

Simplifying
x = -67.839743178


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.839743178, -67.839743178}

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