(x+2)*(x+3)=208

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Solution for (x+2)*(x+3)=208 equation: 


Simplifying
(x + 2)(x + 3) = 208

Reorder the terms:
(2 + x)(x + 3) = 208

Reorder the terms:
(2 + x)(3 + x) = 208

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 208
((3 * 2 + x * 2) + x(3 + x)) = 208
((6 + 2x) + x(3 + x)) = 208
(6 + 2x + (3 * x + x * x)) = 208
(6 + 2x + (3x + x2)) = 208

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 208

Solving
6 + 5x + x2 = 208

Solving for variable 'x'.

Reorder the terms:
6 + -208 + 5x + x2 = 208 + -208

Combine like terms: 6 + -208 = -202
-202 + 5x + x2 = 208 + -208

Combine like terms: 208 + -208 = 0
-202 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '202' to each side of the equation.
-202 + 5x + 202 + x2 = 0 + 202

Reorder the terms:
-202 + 202 + 5x + x2 = 0 + 202

Combine like terms: -202 + 202 = 0
0 + 5x + x2 = 0 + 202
5x + x2 = 0 + 202

Combine like terms: 0 + 202 = 202
5x + x2 = 202

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 = 202 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 202 + 6.25

Combine like terms: 202 + 6.25 = 208.25
6.25 + 5x + x2 = 208.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 208.25

Calculate the square root of the right side: 14.43086969

Break this problem into two subproblems by setting 
(x + 2.5) equal to 14.43086969 and -14.43086969.


Subproblem 1
x + 2.5 = 14.43086969

Simplifying
x + 2.5 = 14.43086969

Reorder the terms:
2.5 + x = 14.43086969

Solving
2.5 + x = 14.43086969

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 = 14.43086969 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 14.43086969 + -2.5
x = 14.43086969 + -2.5

Combine like terms: 14.43086969 + -2.5 = 11.93086969
x = 11.93086969

Simplifying
x = 11.93086969


Subproblem 2
x + 2.5 = -14.43086969

Simplifying
x + 2.5 = -14.43086969

Reorder the terms:
2.5 + x = -14.43086969

Solving
2.5 + x = -14.43086969

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 = -14.43086969 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -14.43086969 + -2.5
x = -14.43086969 + -2.5

Combine like terms: -14.43086969 + -2.5 = -16.93086969
x = -16.93086969

Simplifying
x = -16.93086969


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.93086969, -16.93086969}

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