(x-8)(x+3)-5=0

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Solution for (x-8)(x+3)-5=0 equation: 


Simplifying
(x + -8)(x + 3) + -5 = 0

Reorder the terms:
(-8 + x)(x + 3) + -5 = 0

Reorder the terms:
(-8 + x)(3 + x) + -5 = 0

Multiply (-8 + x) * (3 + x)
(-8(3 + x) + x(3 + x)) + -5 = 0
((3 * -8 + x * -8) + x(3 + x)) + -5 = 0
((-24 + -8x) + x(3 + x)) + -5 = 0
(-24 + -8x + (3 * x + x * x)) + -5 = 0
(-24 + -8x + (3x + x2)) + -5 = 0

Combine like terms: -8x + 3x = -5x
(-24 + -5x + x2) + -5 = 0

Reorder the terms:
-24 + -5 + -5x + x2 = 0

Combine like terms: -24 + -5 = -29
-29 + -5x + x2 = 0

Solving
-29 + -5x + x2 = 0

Solving for variable 'x'.

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 = 8.437171044
x = 8.437171044

Simplifying
x = 8.437171044


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 = -3.437171044
x = -3.437171044

Simplifying
x = -3.437171044


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

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