2x^2-24x-32=0

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Solution for 2x^2-24x-32=0 equation: 


Simplifying
2x2 + -24x + -32 = 0

Reorder the terms:
-32 + -24x + 2x2 = 0

Solving
-32 + -24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -12x + x2 = 0

Solving
-16 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -12x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -12x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -12x + x2 = 0 + 16
-12x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-12x + x2 = 16

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 16 + 36

Reorder the terms:
36 + -12x + x2 = 16 + 36

Combine like terms: 16 + 36 = 52
36 + -12x + x2 = 52

Factor a perfect square on the left side:
(x + -6)(x + -6) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + -6) equal to 7.211102551 and -7.211102551.


Subproblem 1
x + -6 = 7.211102551

Simplifying
x + -6 = 7.211102551

Reorder the terms:
-6 + x = 7.211102551

Solving
-6 + x = 7.211102551

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 7.211102551 + 6

Combine like terms: -6 + 6 = 0
0 + x = 7.211102551 + 6
x = 7.211102551 + 6

Combine like terms: 7.211102551 + 6 = 13.211102551
x = 13.211102551

Simplifying
x = 13.211102551


Subproblem 2
x + -6 = -7.211102551

Simplifying
x + -6 = -7.211102551

Reorder the terms:
-6 + x = -7.211102551

Solving
-6 + x = -7.211102551

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -7.211102551 + 6

Combine like terms: -6 + 6 = 0
0 + x = -7.211102551 + 6
x = -7.211102551 + 6

Combine like terms: -7.211102551 + 6 = -1.211102551
x = -1.211102551

Simplifying
x = -1.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.211102551, -1.211102551}
Solution
x = {13.211102551, -1.211102551}

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