2x^2-16x-192=0

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Solution for 2x^2-16x-192=0 equation: 


Simplifying
2x2 + -16x + -192 = 0

Reorder the terms:
-192 + -16x + 2x2 = 0

Solving
-192 + -16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-96 + -8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-96 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-96 + -8x + x2 = 0

Solving
-96 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + -8x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + -8x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + -8x + x2 = 0 + 96
-8x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
-8x + x2 = 96

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 96 + 16

Reorder the terms:
16 + -8x + x2 = 96 + 16

Combine like terms: 96 + 16 = 112
16 + -8x + x2 = 112

Factor a perfect square on the left side:
(x + -4)(x + -4) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(x + -4) equal to 10.583005244 and -10.583005244.


Subproblem 1
x + -4 = 10.583005244

Simplifying
x + -4 = 10.583005244

Reorder the terms:
-4 + x = 10.583005244

Solving
-4 + x = 10.583005244

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 10.583005244 + 4

Combine like terms: -4 + 4 = 0
0 + x = 10.583005244 + 4
x = 10.583005244 + 4

Combine like terms: 10.583005244 + 4 = 14.583005244
x = 14.583005244

Simplifying
x = 14.583005244


Subproblem 2
x + -4 = -10.583005244

Simplifying
x + -4 = -10.583005244

Reorder the terms:
-4 + x = -10.583005244

Solving
-4 + x = -10.583005244

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -10.583005244 + 4

Combine like terms: -4 + 4 = 0
0 + x = -10.583005244 + 4
x = -10.583005244 + 4

Combine like terms: -10.583005244 + 4 = -6.583005244
x = -6.583005244

Simplifying
x = -6.583005244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.583005244, -6.583005244}
Solution
x = {14.583005244, -6.583005244}

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