x^2-36x+27=0

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Solution for x^2-36x+27=0 equation: 


Simplifying
x2 + -36x + 27 = 0

Reorder the terms:
27 + -36x + x2 = 0

Solving
27 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -36x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + -36x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -36x + x2 = 0 + -27
-36x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-36x + x2 = -27

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 = -27 + 324

Reorder the terms:
324 + -36x + x2 = -27 + 324

Combine like terms: -27 + 324 = 297
324 + -36x + x2 = 297

Factor a perfect square on the left side:
(x + -18)(x + -18) = 297

Calculate the square root of the right side: 17.23368794

Break this problem into two subproblems by setting 
(x + -18) equal to 17.23368794 and -17.23368794.


Subproblem 1
x + -18 = 17.23368794

Simplifying
x + -18 = 17.23368794

Reorder the terms:
-18 + x = 17.23368794

Solving
-18 + x = 17.23368794

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 = 17.23368794 + 18

Combine like terms: -18 + 18 = 0
0 + x = 17.23368794 + 18
x = 17.23368794 + 18

Combine like terms: 17.23368794 + 18 = 35.23368794
x = 35.23368794

Simplifying
x = 35.23368794


Subproblem 2
x + -18 = -17.23368794

Simplifying
x + -18 = -17.23368794

Reorder the terms:
-18 + x = -17.23368794

Solving
-18 + x = -17.23368794

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 = -17.23368794 + 18

Combine like terms: -18 + 18 = 0
0 + x = -17.23368794 + 18
x = -17.23368794 + 18

Combine like terms: -17.23368794 + 18 = 0.76631206
x = 0.76631206

Simplifying
x = 0.76631206


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.23368794, 0.76631206}

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