[(3+x)*(2+x)]=8

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Solution for [(3+x)*(2+x)]=8 equation: 


Simplifying
[(3 + x)(2 + x)] = 8

Multiply (3 + x) * (2 + x)
[(3(2 + x) + x(2 + x))] = 8
[((2 * 3 + x * 3) + x(2 + x))] = 8
[((6 + 3x) + x(2 + x))] = 8
[(6 + 3x + (2 * x + x * x))] = 8
[(6 + 3x + (2x + x2))] = 8

Combine like terms: 3x + 2x = 5x
[(6 + 5x + x2)] = 8
[6 + 5x + x2] = 8

Remove brackets around [6 + 5x + x2]
6 + 5x + x2 = 8

Solving
6 + 5x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
6 + -8 + 5x + x2 = 8 + -8

Combine like terms: 6 + -8 = -2
-2 + 5x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-2 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5x + x2 = 0 + 2
5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
5x + x2 = 2

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + 5x + x2 = 8.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
x + 2.5 = 2.872281323

Simplifying
x + 2.5 = 2.872281323

Reorder the terms:
2.5 + x = 2.872281323

Solving
2.5 + x = 2.872281323

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.872281323 + -2.5
x = 2.872281323 + -2.5

Combine like terms: 2.872281323 + -2.5 = 0.372281323
x = 0.372281323

Simplifying
x = 0.372281323


Subproblem 2
x + 2.5 = -2.872281323

Simplifying
x + 2.5 = -2.872281323

Reorder the terms:
2.5 + x = -2.872281323

Solving
2.5 + x = -2.872281323

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.872281323 + -2.5
x = -2.872281323 + -2.5

Combine like terms: -2.872281323 + -2.5 = -5.372281323
x = -5.372281323

Simplifying
x = -5.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.372281323, -5.372281323}

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