A^2+(A+2)(A+2)=96

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Solution for A^2+(A+2)(A+2)=96 equation: 


Simplifying
A2 + (A + 2)(A + 2) = 96

Reorder the terms:
A2 + (2 + A)(A + 2) = 96

Reorder the terms:
A2 + (2 + A)(2 + A) = 96

Multiply (2 + A) * (2 + A)
A2 + (2(2 + A) + A(2 + A)) = 96
A2 + ((2 * 2 + A * 2) + A(2 + A)) = 96
A2 + ((4 + 2A) + A(2 + A)) = 96
A2 + (4 + 2A + (2 * A + A * A)) = 96
A2 + (4 + 2A + (2A + A2)) = 96

Combine like terms: 2A + 2A = 4A
A2 + (4 + 4A + A2) = 96

Reorder the terms:
4 + 4A + A2 + A2 = 96

Combine like terms: A2 + A2 = 2A2
4 + 4A + 2A2 = 96

Solving
4 + 4A + 2A2 = 96

Solving for variable 'A'.

Reorder the terms:
4 + -96 + 4A + 2A2 = 96 + -96

Combine like terms: 4 + -96 = -92
-92 + 4A + 2A2 = 96 + -96

Combine like terms: 96 + -96 = 0
-92 + 4A + 2A2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-46 + 2A + A2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-46 + 2A + A2)' equal to zero and attempt to solve:

Simplifying
-46 + 2A + A2 = 0

Solving
-46 + 2A + A2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 2A + 46 + A2 = 0 + 46

Reorder the terms:
-46 + 46 + 2A + A2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 2A + A2 = 0 + 46
2A + A2 = 0 + 46

Combine like terms: 0 + 46 = 46
2A + A2 = 46

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

Add '1' to each side of the equation.
2A + 1 + A2 = 46 + 1

Reorder the terms:
1 + 2A + A2 = 46 + 1

Combine like terms: 46 + 1 = 47
1 + 2A + A2 = 47

Factor a perfect square on the left side:
(A + 1)(A + 1) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(A + 1) equal to 6.8556546 and -6.8556546.


Subproblem 1
A + 1 = 6.8556546

Simplifying
A + 1 = 6.8556546

Reorder the terms:
1 + A = 6.8556546

Solving
1 + A = 6.8556546

Solving for variable 'A'.

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

Add '-1' to each side of the equation.
1 + -1 + A = 6.8556546 + -1

Combine like terms: 1 + -1 = 0
0 + A = 6.8556546 + -1
A = 6.8556546 + -1

Combine like terms: 6.8556546 + -1 = 5.8556546
A = 5.8556546

Simplifying
A = 5.8556546


Subproblem 2
A + 1 = -6.8556546

Simplifying
A + 1 = -6.8556546

Reorder the terms:
1 + A = -6.8556546

Solving
1 + A = -6.8556546

Solving for variable 'A'.

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

Add '-1' to each side of the equation.
1 + -1 + A = -6.8556546 + -1

Combine like terms: 1 + -1 = 0
0 + A = -6.8556546 + -1
A = -6.8556546 + -1

Combine like terms: -6.8556546 + -1 = -7.8556546
A = -7.8556546

Simplifying
A = -7.8556546


Solution
The solution to the problem is based on the solutions
from the subproblems.
A = {5.8556546, -7.8556546}
Solution
A = {5.8556546, -7.8556546}

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