8x^2-32x-192=0

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Solution for 8x^2-32x-192=0 equation: 


Simplifying
8x2 + -32x + -192 = 0

Reorder the terms:
-192 + -32x + 8x2 = 0

Solving
-192 + -32x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-24 + -4x + x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-24 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + -4x + x2 = 0

Solving
-24 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -4x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -4x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -4x + x2 = 0 + 24
-4x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-4x + x2 = 24

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 24 + 4

Reorder the terms:
4 + -4x + x2 = 24 + 4

Combine like terms: 24 + 4 = 28
4 + -4x + x2 = 28

Factor a perfect square on the left side:
(x + -2)(x + -2) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -2) equal to 5.291502622 and -5.291502622.


Subproblem 1
x + -2 = 5.291502622

Simplifying
x + -2 = 5.291502622

Reorder the terms:
-2 + x = 5.291502622

Solving
-2 + x = 5.291502622

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 5.291502622 + 2

Combine like terms: -2 + 2 = 0
0 + x = 5.291502622 + 2
x = 5.291502622 + 2

Combine like terms: 5.291502622 + 2 = 7.291502622
x = 7.291502622

Simplifying
x = 7.291502622


Subproblem 2
x + -2 = -5.291502622

Simplifying
x + -2 = -5.291502622

Reorder the terms:
-2 + x = -5.291502622

Solving
-2 + x = -5.291502622

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -5.291502622 + 2

Combine like terms: -2 + 2 = 0
0 + x = -5.291502622 + 2
x = -5.291502622 + 2

Combine like terms: -5.291502622 + 2 = -3.291502622
x = -3.291502622

Simplifying
x = -3.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.291502622, -3.291502622}
Solution
x = {7.291502622, -3.291502622}

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