x^2+36x+225=0

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Solution for x^2+36x+225=0 equation: 


Simplifying
x2 + 36x + 225 = 0

Reorder the terms:
225 + 36x + x2 = 0

Solving
225 + 36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-225' to each side of the equation.
225 + 36x + -225 + x2 = 0 + -225

Reorder the terms:
225 + -225 + 36x + x2 = 0 + -225

Combine like terms: 225 + -225 = 0
0 + 36x + x2 = 0 + -225
36x + x2 = 0 + -225

Combine like terms: 0 + -225 = -225
36x + x2 = -225

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 = -225 + 324

Reorder the terms:
324 + 36x + x2 = -225 + 324

Combine like terms: -225 + 324 = 99
324 + 36x + x2 = 99

Factor a perfect square on the left side:
(x + 18)(x + 18) = 99

Calculate the square root of the right side: 9.949874371

Break this problem into two subproblems by setting 
(x + 18) equal to 9.949874371 and -9.949874371.


Subproblem 1
x + 18 = 9.949874371

Simplifying
x + 18 = 9.949874371

Reorder the terms:
18 + x = 9.949874371

Solving
18 + x = 9.949874371

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 = 9.949874371 + -18

Combine like terms: 18 + -18 = 0
0 + x = 9.949874371 + -18
x = 9.949874371 + -18

Combine like terms: 9.949874371 + -18 = -8.050125629
x = -8.050125629

Simplifying
x = -8.050125629


Subproblem 2
x + 18 = -9.949874371

Simplifying
x + 18 = -9.949874371

Reorder the terms:
18 + x = -9.949874371

Solving
18 + x = -9.949874371

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 = -9.949874371 + -18

Combine like terms: 18 + -18 = 0
0 + x = -9.949874371 + -18
x = -9.949874371 + -18

Combine like terms: -9.949874371 + -18 = -27.949874371
x = -27.949874371

Simplifying
x = -27.949874371


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.050125629, -27.949874371}

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