2x^2-36x+32=0

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Solution for 2x^2-36x+32=0 equation: 


Simplifying
2x2 + -36x + 32 = 0

Reorder the terms:
32 + -36x + 2x2 = 0

Solving
32 + -36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -18x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -18x + x2)' equal to zero and attempt to solve:

Simplifying
16 + -18x + x2 = 0

Solving
16 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -18x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -18x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -18x + x2 = 0 + -16
-18x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-18x + x2 = -16

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 = -16 + 81

Reorder the terms:
81 + -18x + x2 = -16 + 81

Combine like terms: -16 + 81 = 65
81 + -18x + x2 = 65

Factor a perfect square on the left side:
(x + -9)(x + -9) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + -9) equal to 8.062257748 and -8.062257748.


Subproblem 1
x + -9 = 8.062257748

Simplifying
x + -9 = 8.062257748

Reorder the terms:
-9 + x = 8.062257748

Solving
-9 + x = 8.062257748

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 = 8.062257748 + 9

Combine like terms: -9 + 9 = 0
0 + x = 8.062257748 + 9
x = 8.062257748 + 9

Combine like terms: 8.062257748 + 9 = 17.062257748
x = 17.062257748

Simplifying
x = 17.062257748


Subproblem 2
x + -9 = -8.062257748

Simplifying
x + -9 = -8.062257748

Reorder the terms:
-9 + x = -8.062257748

Solving
-9 + x = -8.062257748

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 = -8.062257748 + 9

Combine like terms: -9 + 9 = 0
0 + x = -8.062257748 + 9
x = -8.062257748 + 9

Combine like terms: -8.062257748 + 9 = 0.937742252
x = 0.937742252

Simplifying
x = 0.937742252


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.062257748, 0.937742252}
Solution
x = {17.062257748, 0.937742252}

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