x^2+36x-360=0

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Solution for x^2+36x-360=0 equation: 


Simplifying
x2 + 36x + -360 = 0

Reorder the terms:
-360 + 36x + x2 = 0

Solving
-360 + 36x + 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 + 36x + 360 + x2 = 0 + 360

Reorder the terms:
-360 + 360 + 36x + x2 = 0 + 360

Combine like terms: -360 + 360 = 0
0 + 36x + x2 = 0 + 360
36x + x2 = 0 + 360

Combine like terms: 0 + 360 = 360
36x + x2 = 360

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 = 360 + 324

Reorder the terms:
324 + 36x + x2 = 360 + 324

Combine like terms: 360 + 324 = 684
324 + 36x + x2 = 684

Factor a perfect square on the left side:
(x + 18)(x + 18) = 684

Calculate the square root of the right side: 26.153393661

Break this problem into two subproblems by setting 
(x + 18) equal to 26.153393661 and -26.153393661.


Subproblem 1
x + 18 = 26.153393661

Simplifying
x + 18 = 26.153393661

Reorder the terms:
18 + x = 26.153393661

Solving
18 + x = 26.153393661

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 = 26.153393661 + -18

Combine like terms: 18 + -18 = 0
0 + x = 26.153393661 + -18
x = 26.153393661 + -18

Combine like terms: 26.153393661 + -18 = 8.153393661
x = 8.153393661

Simplifying
x = 8.153393661


Subproblem 2
x + 18 = -26.153393661

Simplifying
x + 18 = -26.153393661

Reorder the terms:
18 + x = -26.153393661

Solving
18 + x = -26.153393661

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 = -26.153393661 + -18

Combine like terms: 18 + -18 = 0
0 + x = -26.153393661 + -18
x = -26.153393661 + -18

Combine like terms: -26.153393661 + -18 = -44.153393661
x = -44.153393661

Simplifying
x = -44.153393661


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.153393661, -44.153393661}

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