x^2-36x-162=0

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Solution for x^2-36x-162=0 equation: 


Simplifying
x2 + -36x + -162 = 0

Reorder the terms:
-162 + -36x + x2 = 0

Solving
-162 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '162' to each side of the equation.
-162 + -36x + 162 + x2 = 0 + 162

Reorder the terms:
-162 + 162 + -36x + x2 = 0 + 162

Combine like terms: -162 + 162 = 0
0 + -36x + x2 = 0 + 162
-36x + x2 = 0 + 162

Combine like terms: 0 + 162 = 162
-36x + x2 = 162

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 = 162 + 324

Reorder the terms:
324 + -36x + x2 = 162 + 324

Combine like terms: 162 + 324 = 486
324 + -36x + x2 = 486

Factor a perfect square on the left side:
(x + -18)(x + -18) = 486

Calculate the square root of the right side: 22.045407685

Break this problem into two subproblems by setting 
(x + -18) equal to 22.045407685 and -22.045407685.


Subproblem 1
x + -18 = 22.045407685

Simplifying
x + -18 = 22.045407685

Reorder the terms:
-18 + x = 22.045407685

Solving
-18 + x = 22.045407685

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 = 22.045407685 + 18

Combine like terms: -18 + 18 = 0
0 + x = 22.045407685 + 18
x = 22.045407685 + 18

Combine like terms: 22.045407685 + 18 = 40.045407685
x = 40.045407685

Simplifying
x = 40.045407685


Subproblem 2
x + -18 = -22.045407685

Simplifying
x + -18 = -22.045407685

Reorder the terms:
-18 + x = -22.045407685

Solving
-18 + x = -22.045407685

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 = -22.045407685 + 18

Combine like terms: -18 + 18 = 0
0 + x = -22.045407685 + 18
x = -22.045407685 + 18

Combine like terms: -22.045407685 + 18 = -4.045407685
x = -4.045407685

Simplifying
x = -4.045407685


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {40.045407685, -4.045407685}

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