(1+x)2x=96

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Solution for (1+x)2x=96 equation: 


Simplifying
(1 + x) * 2x = 96

Reorder the terms for easier multiplication:
2x(1 + x) = 96
(1 * 2x + x * 2x) = 96
(2x + 2x2) = 96

Solving
2x + 2x2 = 96

Solving for variable 'x'.

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

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

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

Ignore the factor 2.

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

Simplifying
-48 + x + x2 = 0

Solving
-48 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 48 + 0.25

Reorder the terms:
0.25 + x + x2 = 48 + 0.25

Combine like terms: 48 + 0.25 = 48.25
0.25 + x + x2 = 48.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
x + 0.5 = 6.946221995

Simplifying
x + 0.5 = 6.946221995

Reorder the terms:
0.5 + x = 6.946221995

Solving
0.5 + x = 6.946221995

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 6.946221995 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.946221995 + -0.5
x = 6.946221995 + -0.5

Combine like terms: 6.946221995 + -0.5 = 6.446221995
x = 6.446221995

Simplifying
x = 6.446221995


Subproblem 2
x + 0.5 = -6.946221995

Simplifying
x + 0.5 = -6.946221995

Reorder the terms:
0.5 + x = -6.946221995

Solving
0.5 + x = -6.946221995

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -6.946221995 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.946221995 + -0.5
x = -6.946221995 + -0.5

Combine like terms: -6.946221995 + -0.5 = -7.446221995
x = -7.446221995

Simplifying
x = -7.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.446221995, -7.446221995}
Solution
x = {6.446221995, -7.446221995}

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