x^2-18x+36=0

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Solution for x^2-18x+36=0 equation: 


Simplifying
x2 + -18x + 36 = 0

Reorder the terms:
36 + -18x + x2 = 0

Solving
36 + -18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -18x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -18x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -18x + x2 = 0 + -36
-18x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-18x + x2 = -36

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -36 + 81

Reorder the terms:
81 + -18x + x2 = -36 + 81

Combine like terms: -36 + 81 = 45
81 + -18x + x2 = 45

Factor a perfect square on the left side:
(x + -9)(x + -9) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -9) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + -9 = 6.708203933

Simplifying
x + -9 = 6.708203933

Reorder the terms:
-9 + x = 6.708203933

Solving
-9 + x = 6.708203933

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + x = 6.708203933 + 9

Combine like terms: -9 + 9 = 0
0 + x = 6.708203933 + 9
x = 6.708203933 + 9

Combine like terms: 6.708203933 + 9 = 15.708203933
x = 15.708203933

Simplifying
x = 15.708203933


Subproblem 2
x + -9 = -6.708203933

Simplifying
x + -9 = -6.708203933

Reorder the terms:
-9 + x = -6.708203933

Solving
-9 + x = -6.708203933

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + x = -6.708203933 + 9

Combine like terms: -9 + 9 = 0
0 + x = -6.708203933 + 9
x = -6.708203933 + 9

Combine like terms: -6.708203933 + 9 = 2.291796067
x = 2.291796067

Simplifying
x = 2.291796067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.708203933, 2.291796067}

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