x^2-36x-396=0

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Solution for x^2-36x-396=0 equation: 


Simplifying
x2 + -36x + -396 = 0

Reorder the terms:
-396 + -36x + x2 = 0

Solving
-396 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '396' to each side of the equation.
-396 + -36x + 396 + x2 = 0 + 396

Reorder the terms:
-396 + 396 + -36x + x2 = 0 + 396

Combine like terms: -396 + 396 = 0
0 + -36x + x2 = 0 + 396
-36x + x2 = 0 + 396

Combine like terms: 0 + 396 = 396
-36x + x2 = 396

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 = 396 + 324

Reorder the terms:
324 + -36x + x2 = 396 + 324

Combine like terms: 396 + 324 = 720
324 + -36x + x2 = 720

Factor a perfect square on the left side:
(x + -18)(x + -18) = 720

Calculate the square root of the right side: 26.83281573

Break this problem into two subproblems by setting 
(x + -18) equal to 26.83281573 and -26.83281573.


Subproblem 1
x + -18 = 26.83281573

Simplifying
x + -18 = 26.83281573

Reorder the terms:
-18 + x = 26.83281573

Solving
-18 + x = 26.83281573

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 = 26.83281573 + 18

Combine like terms: -18 + 18 = 0
0 + x = 26.83281573 + 18
x = 26.83281573 + 18

Combine like terms: 26.83281573 + 18 = 44.83281573
x = 44.83281573

Simplifying
x = 44.83281573


Subproblem 2
x + -18 = -26.83281573

Simplifying
x + -18 = -26.83281573

Reorder the terms:
-18 + x = -26.83281573

Solving
-18 + x = -26.83281573

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 = -26.83281573 + 18

Combine like terms: -18 + 18 = 0
0 + x = -26.83281573 + 18
x = -26.83281573 + 18

Combine like terms: -26.83281573 + 18 = -8.83281573
x = -8.83281573

Simplifying
x = -8.83281573


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {44.83281573, -8.83281573}

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