(x+5)(x+3)=5

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Solution for (x+5)(x+3)=5 equation: 


Simplifying
(x + 5)(x + 3) = 5

Reorder the terms:
(5 + x)(x + 3) = 5

Reorder the terms:
(5 + x)(3 + x) = 5

Multiply (5 + x) * (3 + x)
(5(3 + x) + x(3 + x)) = 5
((3 * 5 + x * 5) + x(3 + x)) = 5
((15 + 5x) + x(3 + x)) = 5
(15 + 5x + (3 * x + x * x)) = 5
(15 + 5x + (3x + x2)) = 5

Combine like terms: 5x + 3x = 8x
(15 + 8x + x2) = 5

Solving
15 + 8x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
15 + -5 + 8x + x2 = 5 + -5

Combine like terms: 15 + -5 = 10
10 + 8x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
10 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 8x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 8x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 8x + x2 = 0 + -10
8x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
8x + x2 = -10

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -10 + 16

Reorder the terms:
16 + 8x + x2 = -10 + 16

Combine like terms: -10 + 16 = 6
16 + 8x + x2 = 6

Factor a perfect square on the left side:
(x + 4)(x + 4) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 4) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + 4 = 2.449489743

Simplifying
x + 4 = 2.449489743

Reorder the terms:
4 + x = 2.449489743

Solving
4 + x = 2.449489743

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 2.449489743 + -4

Combine like terms: 4 + -4 = 0
0 + x = 2.449489743 + -4
x = 2.449489743 + -4

Combine like terms: 2.449489743 + -4 = -1.550510257
x = -1.550510257

Simplifying
x = -1.550510257


Subproblem 2
x + 4 = -2.449489743

Simplifying
x + 4 = -2.449489743

Reorder the terms:
4 + x = -2.449489743

Solving
4 + x = -2.449489743

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -2.449489743 + -4

Combine like terms: 4 + -4 = 0
0 + x = -2.449489743 + -4
x = -2.449489743 + -4

Combine like terms: -2.449489743 + -4 = -6.449489743
x = -6.449489743

Simplifying
x = -6.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.550510257, -6.449489743}

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