x^2-36x-180=0

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Solution for x^2-36x-180=0 equation: 


Simplifying
x2 + -36x + -180 = 0

Reorder the terms:
-180 + -36x + x2 = 0

Solving
-180 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + -36x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + -36x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -36x + x2 = 0 + 180
-36x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
-36x + x2 = 180

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 = 180 + 324

Reorder the terms:
324 + -36x + x2 = 180 + 324

Combine like terms: 180 + 324 = 504
324 + -36x + x2 = 504

Factor a perfect square on the left side:
(x + -18)(x + -18) = 504

Calculate the square root of the right side: 22.449944321

Break this problem into two subproblems by setting 
(x + -18) equal to 22.449944321 and -22.449944321.


Subproblem 1
x + -18 = 22.449944321

Simplifying
x + -18 = 22.449944321

Reorder the terms:
-18 + x = 22.449944321

Solving
-18 + x = 22.449944321

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 = 22.449944321 + 18

Combine like terms: -18 + 18 = 0
0 + x = 22.449944321 + 18
x = 22.449944321 + 18

Combine like terms: 22.449944321 + 18 = 40.449944321
x = 40.449944321

Simplifying
x = 40.449944321


Subproblem 2
x + -18 = -22.449944321

Simplifying
x + -18 = -22.449944321

Reorder the terms:
-18 + x = -22.449944321

Solving
-18 + x = -22.449944321

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 = -22.449944321 + 18

Combine like terms: -18 + 18 = 0
0 + x = -22.449944321 + 18
x = -22.449944321 + 18

Combine like terms: -22.449944321 + 18 = -4.449944321
x = -4.449944321

Simplifying
x = -4.449944321


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {40.449944321, -4.449944321}

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