2(x^2+2x-96)=0

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Solution for 2(x^2+2x-96)=0 equation: 


Simplifying
2(x2 + 2x + -96) = 0

Reorder the terms:
2(-96 + 2x + x2) = 0
(-96 * 2 + 2x * 2 + x2 * 2) = 0
(-192 + 4x + 2x2) = 0

Solving
-192 + 4x + 2x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-96 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-96 + 2x + x2 = 0

Solving
-96 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 2x + 96 + x2 = 0 + 96

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

Combine like terms: -96 + 96 = 0
0 + 2x + x2 = 0 + 96
2x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
2x + x2 = 96

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 96 + 1

Reorder the terms:
1 + 2x + x2 = 96 + 1

Combine like terms: 96 + 1 = 97
1 + 2x + x2 = 97

Factor a perfect square on the left side:
(x + 1)(x + 1) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + 1) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + 1 = 9.848857802

Simplifying
x + 1 = 9.848857802

Reorder the terms:
1 + x = 9.848857802

Solving
1 + x = 9.848857802

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 9.848857802 + -1

Combine like terms: 1 + -1 = 0
0 + x = 9.848857802 + -1
x = 9.848857802 + -1

Combine like terms: 9.848857802 + -1 = 8.848857802
x = 8.848857802

Simplifying
x = 8.848857802


Subproblem 2
x + 1 = -9.848857802

Simplifying
x + 1 = -9.848857802

Reorder the terms:
1 + x = -9.848857802

Solving
1 + x = -9.848857802

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -9.848857802 + -1

Combine like terms: 1 + -1 = 0
0 + x = -9.848857802 + -1
x = -9.848857802 + -1

Combine like terms: -9.848857802 + -1 = -10.848857802
x = -10.848857802

Simplifying
x = -10.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.848857802, -10.848857802}
Solution
x = {8.848857802, -10.848857802}

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