2x^2-28x+32=0

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Solution for 2x^2-28x+32=0 equation: 


Simplifying
2x2 + -28x + 32 = 0

Reorder the terms:
32 + -28x + 2x2 = 0

Solving
32 + -28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
16 + -14x + x2 = 0

Solving
16 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -14x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -14x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -14x + x2 = 0 + -16
-14x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-14x + x2 = -16

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -16 + 49

Reorder the terms:
49 + -14x + x2 = -16 + 49

Combine like terms: -16 + 49 = 33
49 + -14x + x2 = 33

Factor a perfect square on the left side:
(x + -7)(x + -7) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -7) equal to 5.744562647 and -5.744562647.


Subproblem 1
x + -7 = 5.744562647

Simplifying
x + -7 = 5.744562647

Reorder the terms:
-7 + x = 5.744562647

Solving
-7 + x = 5.744562647

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 5.744562647 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.744562647 + 7
x = 5.744562647 + 7

Combine like terms: 5.744562647 + 7 = 12.744562647
x = 12.744562647

Simplifying
x = 12.744562647


Subproblem 2
x + -7 = -5.744562647

Simplifying
x + -7 = -5.744562647

Reorder the terms:
-7 + x = -5.744562647

Solving
-7 + x = -5.744562647

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -5.744562647 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.744562647 + 7
x = -5.744562647 + 7

Combine like terms: -5.744562647 + 7 = 1.255437353
x = 1.255437353

Simplifying
x = 1.255437353


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.744562647, 1.255437353}
Solution
x = {12.744562647, 1.255437353}

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