x^2+36x+36=0

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


Simplifying
x2 + 36x + 36 = 0

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

Solving
36 + 36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -36 + 324

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

Combine like terms: -36 + 324 = 288
324 + 36x + x2 = 288

Factor a perfect square on the left side:
(x + 18)(x + 18) = 288

Calculate the square root of the right side: 16.970562748

Break this problem into two subproblems by setting 
(x + 18) equal to 16.970562748 and -16.970562748.


Subproblem 1
x + 18 = 16.970562748

Simplifying
x + 18 = 16.970562748

Reorder the terms:
18 + x = 16.970562748

Solving
18 + x = 16.970562748

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 = 16.970562748 + -18

Combine like terms: 18 + -18 = 0
0 + x = 16.970562748 + -18
x = 16.970562748 + -18

Combine like terms: 16.970562748 + -18 = -1.029437252
x = -1.029437252

Simplifying
x = -1.029437252


Subproblem 2
x + 18 = -16.970562748

Simplifying
x + 18 = -16.970562748

Reorder the terms:
18 + x = -16.970562748

Solving
18 + x = -16.970562748

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 = -16.970562748 + -18

Combine like terms: 18 + -18 = 0
0 + x = -16.970562748 + -18
x = -16.970562748 + -18

Combine like terms: -16.970562748 + -18 = -34.970562748
x = -34.970562748

Simplifying
x = -34.970562748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.029437252, -34.970562748}

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