x^2+36x-432=0

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Solution for x^2+36x-432=0 equation: 


Simplifying
x2 + 36x + -432 = 0

Reorder the terms:
-432 + 36x + x2 = 0

Solving
-432 + 36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '432' to each side of the equation.
-432 + 36x + 432 + x2 = 0 + 432

Reorder the terms:
-432 + 432 + 36x + x2 = 0 + 432

Combine like terms: -432 + 432 = 0
0 + 36x + x2 = 0 + 432
36x + x2 = 0 + 432

Combine like terms: 0 + 432 = 432
36x + x2 = 432

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 = 432 + 324

Reorder the terms:
324 + 36x + x2 = 432 + 324

Combine like terms: 432 + 324 = 756
324 + 36x + x2 = 756

Factor a perfect square on the left side:
(x + 18)(x + 18) = 756

Calculate the square root of the right side: 27.49545417

Break this problem into two subproblems by setting 
(x + 18) equal to 27.49545417 and -27.49545417.


Subproblem 1
x + 18 = 27.49545417

Simplifying
x + 18 = 27.49545417

Reorder the terms:
18 + x = 27.49545417

Solving
18 + x = 27.49545417

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 = 27.49545417 + -18

Combine like terms: 18 + -18 = 0
0 + x = 27.49545417 + -18
x = 27.49545417 + -18

Combine like terms: 27.49545417 + -18 = 9.49545417
x = 9.49545417

Simplifying
x = 9.49545417


Subproblem 2
x + 18 = -27.49545417

Simplifying
x + 18 = -27.49545417

Reorder the terms:
18 + x = -27.49545417

Solving
18 + x = -27.49545417

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 = -27.49545417 + -18

Combine like terms: 18 + -18 = 0
0 + x = -27.49545417 + -18
x = -27.49545417 + -18

Combine like terms: -27.49545417 + -18 = -45.49545417
x = -45.49545417

Simplifying
x = -45.49545417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.49545417, -45.49545417}

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