2x^2-36x+36=0

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


Simplifying
2x2 + -36x + 36 = 0

Reorder the terms:
36 + -36x + 2x2 = 0

Solving
36 + -36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -18x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(18 + -18x + x2)' equal to zero and attempt to solve:

Simplifying
18 + -18x + x2 = 0

Solving
18 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -18 + 81

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

Combine like terms: -18 + 81 = 63
81 + -18x + x2 = 63

Factor a perfect square on the left side:
(x + -9)(x + -9) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + -9) equal to 7.937253933 and -7.937253933.


Subproblem 1
x + -9 = 7.937253933

Simplifying
x + -9 = 7.937253933

Reorder the terms:
-9 + x = 7.937253933

Solving
-9 + x = 7.937253933

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 = 7.937253933 + 9

Combine like terms: -9 + 9 = 0
0 + x = 7.937253933 + 9
x = 7.937253933 + 9

Combine like terms: 7.937253933 + 9 = 16.937253933
x = 16.937253933

Simplifying
x = 16.937253933


Subproblem 2
x + -9 = -7.937253933

Simplifying
x + -9 = -7.937253933

Reorder the terms:
-9 + x = -7.937253933

Solving
-9 + x = -7.937253933

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 = -7.937253933 + 9

Combine like terms: -9 + 9 = 0
0 + x = -7.937253933 + 9
x = -7.937253933 + 9

Combine like terms: -7.937253933 + 9 = 1.062746067
x = 1.062746067

Simplifying
x = 1.062746067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.937253933, 1.062746067}
Solution
x = {16.937253933, 1.062746067}

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