(x+8)(x-3)=5

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Solution for (x+8)(x-3)=5 equation: 


Simplifying
(x + 8)(x + -3) = 5

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

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

Multiply (8 + x) * (-3 + x)
(8(-3 + x) + x(-3 + x)) = 5
((-3 * 8 + x * 8) + x(-3 + x)) = 5
((-24 + 8x) + x(-3 + x)) = 5
(-24 + 8x + (-3 * x + x * x)) = 5
(-24 + 8x + (-3x + x2)) = 5

Combine like terms: 8x + -3x = 5x
(-24 + 5x + x2) = 5

Solving
-24 + 5x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-24 + -5 + 5x + x2 = 5 + -5

Combine like terms: -24 + -5 = -29
-29 + 5x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-29 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 5x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 5x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 5x + x2 = 0 + 29
5x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
5x + x2 = 29

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 = 29 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 29 + 6.25

Combine like terms: 29 + 6.25 = 35.25
6.25 + 5x + x2 = 35.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.937171044 and -5.937171044.


Subproblem 1
x + 2.5 = 5.937171044

Simplifying
x + 2.5 = 5.937171044

Reorder the terms:
2.5 + x = 5.937171044

Solving
2.5 + x = 5.937171044

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 = 5.937171044 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.937171044 + -2.5
x = 5.937171044 + -2.5

Combine like terms: 5.937171044 + -2.5 = 3.437171044
x = 3.437171044

Simplifying
x = 3.437171044


Subproblem 2
x + 2.5 = -5.937171044

Simplifying
x + 2.5 = -5.937171044

Reorder the terms:
2.5 + x = -5.937171044

Solving
2.5 + x = -5.937171044

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 = -5.937171044 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.937171044 + -2.5
x = -5.937171044 + -2.5

Combine like terms: -5.937171044 + -2.5 = -8.437171044
x = -8.437171044

Simplifying
x = -8.437171044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.437171044, -8.437171044}

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