2x^2-44x-32=0

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Solution for 2x^2-44x-32=0 equation: 


Simplifying
2x2 + -44x + -32 = 0

Reorder the terms:
-32 + -44x + 2x2 = 0

Solving
-32 + -44x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -22x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + -22x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -22x + x2 = 0

Solving
-16 + -22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -22x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -22x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -22x + x2 = 0 + 16
-22x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-22x + x2 = 16

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = 16 + 121

Reorder the terms:
121 + -22x + x2 = 16 + 121

Combine like terms: 16 + 121 = 137
121 + -22x + x2 = 137

Factor a perfect square on the left side:
(x + -11)(x + -11) = 137

Calculate the square root of the right side: 11.704699911

Break this problem into two subproblems by setting 
(x + -11) equal to 11.704699911 and -11.704699911.


Subproblem 1
x + -11 = 11.704699911

Simplifying
x + -11 = 11.704699911

Reorder the terms:
-11 + x = 11.704699911

Solving
-11 + x = 11.704699911

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 11.704699911 + 11

Combine like terms: -11 + 11 = 0
0 + x = 11.704699911 + 11
x = 11.704699911 + 11

Combine like terms: 11.704699911 + 11 = 22.704699911
x = 22.704699911

Simplifying
x = 22.704699911


Subproblem 2
x + -11 = -11.704699911

Simplifying
x + -11 = -11.704699911

Reorder the terms:
-11 + x = -11.704699911

Solving
-11 + x = -11.704699911

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -11.704699911 + 11

Combine like terms: -11 + 11 = 0
0 + x = -11.704699911 + 11
x = -11.704699911 + 11

Combine like terms: -11.704699911 + 11 = -0.704699911
x = -0.704699911

Simplifying
x = -0.704699911


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.704699911, -0.704699911}
Solution
x = {22.704699911, -0.704699911}

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