(x+8)(x+5)=30

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Solution for (x+8)(x+5)=30 equation: 


Simplifying
(x + 8)(x + 5) = 30

Reorder the terms:
(8 + x)(x + 5) = 30

Reorder the terms:
(8 + x)(5 + x) = 30

Multiply (8 + x) * (5 + x)
(8(5 + x) + x(5 + x)) = 30
((5 * 8 + x * 8) + x(5 + x)) = 30
((40 + 8x) + x(5 + x)) = 30
(40 + 8x + (5 * x + x * x)) = 30
(40 + 8x + (5x + x2)) = 30

Combine like terms: 8x + 5x = 13x
(40 + 13x + x2) = 30

Solving
40 + 13x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
40 + -30 + 13x + x2 = 30 + -30

Combine like terms: 40 + -30 = 10
10 + 13x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
10 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 13x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 13x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 13x + x2 = 0 + -10
13x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
13x + x2 = -10

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = -10 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -10 + 42.25

Combine like terms: -10 + 42.25 = 32.25
42.25 + 13x + x2 = 32.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 6.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
x + 6.5 = 5.678908346

Simplifying
x + 6.5 = 5.678908346

Reorder the terms:
6.5 + x = 5.678908346

Solving
6.5 + x = 5.678908346

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 5.678908346 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 5.678908346 + -6.5
x = 5.678908346 + -6.5

Combine like terms: 5.678908346 + -6.5 = -0.821091654
x = -0.821091654

Simplifying
x = -0.821091654


Subproblem 2
x + 6.5 = -5.678908346

Simplifying
x + 6.5 = -5.678908346

Reorder the terms:
6.5 + x = -5.678908346

Solving
6.5 + x = -5.678908346

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -5.678908346 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -5.678908346 + -6.5
x = -5.678908346 + -6.5

Combine like terms: -5.678908346 + -6.5 = -12.178908346
x = -12.178908346

Simplifying
x = -12.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.821091654, -12.178908346}

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