x^2-36x-324=0

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Solution for x^2-36x-324=0 equation: 


Simplifying
x2 + -36x + -324 = 0

Reorder the terms:
-324 + -36x + x2 = 0

Solving
-324 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '324' to each side of the equation.
-324 + -36x + 324 + x2 = 0 + 324

Reorder the terms:
-324 + 324 + -36x + x2 = 0 + 324

Combine like terms: -324 + 324 = 0
0 + -36x + x2 = 0 + 324
-36x + x2 = 0 + 324

Combine like terms: 0 + 324 = 324
-36x + x2 = 324

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 = 324 + 324

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

Combine like terms: 324 + 324 = 648
324 + -36x + x2 = 648

Factor a perfect square on the left side:
(x + -18)(x + -18) = 648

Calculate the square root of the right side: 25.455844123

Break this problem into two subproblems by setting 
(x + -18) equal to 25.455844123 and -25.455844123.


Subproblem 1
x + -18 = 25.455844123

Simplifying
x + -18 = 25.455844123

Reorder the terms:
-18 + x = 25.455844123

Solving
-18 + x = 25.455844123

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 = 25.455844123 + 18

Combine like terms: -18 + 18 = 0
0 + x = 25.455844123 + 18
x = 25.455844123 + 18

Combine like terms: 25.455844123 + 18 = 43.455844123
x = 43.455844123

Simplifying
x = 43.455844123


Subproblem 2
x + -18 = -25.455844123

Simplifying
x + -18 = -25.455844123

Reorder the terms:
-18 + x = -25.455844123

Solving
-18 + x = -25.455844123

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 = -25.455844123 + 18

Combine like terms: -18 + 18 = 0
0 + x = -25.455844123 + 18
x = -25.455844123 + 18

Combine like terms: -25.455844123 + 18 = -7.455844123
x = -7.455844123

Simplifying
x = -7.455844123


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {43.455844123, -7.455844123}

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