(x-7)(x+8)=5

Solution for (x-7)(x+8)=5 equation:

Simplifying
(x + -7)(x + 8) = 5

Reorder the terms:
(-7 + x)(x + 8) = 5

Reorder the terms:
(-7 + x)(8 + x) = 5

Multiply (-7 + x) * (8 + x)
(-7(8 + x) + x(8 + x)) = 5
((8 * -7 + x * -7) + x(8 + x)) = 5
((-56 + -7x) + x(8 + x)) = 5
(-56 + -7x + (8 * x + x * x)) = 5
(-56 + -7x + (8x + x2)) = 5

Combine like terms: -7x + 8x = 1x
(-56 + 1x + x2) = 5

Solving
-56 + 1x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-56 + -5 + 1x + x2 = 5 + -5

Combine like terms: -56 + -5 = -61
-61 + 1x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-61 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + 1x + 61 + x2 = 0 + 61

Reorder the terms:
-61 + 61 + 1x + x2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + 1x + x2 = 0 + 61
1x + x2 = 0 + 61

Combine like terms: 0 + 61 = 61
1x + x2 = 61

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 61 + 0.25

Reorder the terms:
0.25 + x + x2 = 61 + 0.25

Combine like terms: 61 + 0.25 = 61.25
0.25 + x + x2 = 61.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 61.25

Calculate the square root of the right side: 7.826237921

Break this problem into two subproblems by setting 
(x + 0.5) equal to 7.826237921 and -7.826237921.

Subproblem 1
x + 0.5 = 7.826237921

Simplifying
x + 0.5 = 7.826237921

Reorder the terms:
0.5 + x = 7.826237921

Solving
0.5 + x = 7.826237921

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 7.826237921 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 7.826237921 + -0.5
x = 7.826237921 + -0.5

Combine like terms: 7.826237921 + -0.5 = 7.326237921
x = 7.326237921

Simplifying
x = 7.326237921

Subproblem 2
x + 0.5 = -7.826237921

Simplifying
x + 0.5 = -7.826237921

Reorder the terms:
0.5 + x = -7.826237921

Solving
0.5 + x = -7.826237921

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -7.826237921 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -7.826237921 + -0.5
x = -7.826237921 + -0.5

Combine like terms: -7.826237921 + -0.5 = -8.326237921
x = -8.326237921

Simplifying
x = -8.326237921

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.326237921, -8.326237921}