2x^2-8x-96=0

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Solution for 2x^2-8x-96=0 equation: 


Simplifying
2x2 + -8x + -96 = 0

Reorder the terms:
-96 + -8x + 2x2 = 0

Solving
-96 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-48 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-48 + -4x + x2 = 0

Solving
-48 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -4x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + -4x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -4x + x2 = 0 + 48
-4x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
-4x + x2 = 48

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 = 48 + 4

Reorder the terms:
4 + -4x + x2 = 48 + 4

Combine like terms: 48 + 4 = 52
4 + -4x + x2 = 52

Factor a perfect square on the left side:
(x + -2)(x + -2) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + -2) equal to 7.211102551 and -7.211102551.


Subproblem 1
x + -2 = 7.211102551

Simplifying
x + -2 = 7.211102551

Reorder the terms:
-2 + x = 7.211102551

Solving
-2 + x = 7.211102551

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 = 7.211102551 + 2

Combine like terms: -2 + 2 = 0
0 + x = 7.211102551 + 2
x = 7.211102551 + 2

Combine like terms: 7.211102551 + 2 = 9.211102551
x = 9.211102551

Simplifying
x = 9.211102551


Subproblem 2
x + -2 = -7.211102551

Simplifying
x + -2 = -7.211102551

Reorder the terms:
-2 + x = -7.211102551

Solving
-2 + x = -7.211102551

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 = -7.211102551 + 2

Combine like terms: -2 + 2 = 0
0 + x = -7.211102551 + 2
x = -7.211102551 + 2

Combine like terms: -7.211102551 + 2 = -5.211102551
x = -5.211102551

Simplifying
x = -5.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.211102551, -5.211102551}
Solution
x = {9.211102551, -5.211102551}

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