x^2+180x+360=0

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Solution for x^2+180x+360=0 equation: 


Simplifying
x2 + 180x + 360 = 0

Reorder the terms:
360 + 180x + x2 = 0

Solving
360 + 180x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-360' to each side of the equation.
360 + 180x + -360 + x2 = 0 + -360

Reorder the terms:
360 + -360 + 180x + x2 = 0 + -360

Combine like terms: 360 + -360 = 0
0 + 180x + x2 = 0 + -360
180x + x2 = 0 + -360

Combine like terms: 0 + -360 = -360
180x + x2 = -360

The x term is 180x.  Take half its coefficient (90).
Square it (8100) and add it to both sides.

Add '8100' to each side of the equation.
180x + 8100 + x2 = -360 + 8100

Reorder the terms:
8100 + 180x + x2 = -360 + 8100

Combine like terms: -360 + 8100 = 7740
8100 + 180x + x2 = 7740

Factor a perfect square on the left side:
(x + 90)(x + 90) = 7740

Calculate the square root of the right side: 87.977269792

Break this problem into two subproblems by setting 
(x + 90) equal to 87.977269792 and -87.977269792.


Subproblem 1
x + 90 = 87.977269792

Simplifying
x + 90 = 87.977269792

Reorder the terms:
90 + x = 87.977269792

Solving
90 + x = 87.977269792

Solving for variable 'x'.

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

Add '-90' to each side of the equation.
90 + -90 + x = 87.977269792 + -90

Combine like terms: 90 + -90 = 0
0 + x = 87.977269792 + -90
x = 87.977269792 + -90

Combine like terms: 87.977269792 + -90 = -2.022730208
x = -2.022730208

Simplifying
x = -2.022730208


Subproblem 2
x + 90 = -87.977269792

Simplifying
x + 90 = -87.977269792

Reorder the terms:
90 + x = -87.977269792

Solving
90 + x = -87.977269792

Solving for variable 'x'.

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

Add '-90' to each side of the equation.
90 + -90 + x = -87.977269792 + -90

Combine like terms: 90 + -90 = 0
0 + x = -87.977269792 + -90
x = -87.977269792 + -90

Combine like terms: -87.977269792 + -90 = -177.977269792
x = -177.977269792

Simplifying
x = -177.977269792


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.022730208, -177.977269792}

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