(x-1)(x+8)=8

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Solution for (x-1)(x+8)=8 equation: 


Simplifying
(x + -1)(x + 8) = 8

Reorder the terms:
(-1 + x)(x + 8) = 8

Reorder the terms:
(-1 + x)(8 + x) = 8

Multiply (-1 + x) * (8 + x)
(-1(8 + x) + x(8 + x)) = 8
((8 * -1 + x * -1) + x(8 + x)) = 8
((-8 + -1x) + x(8 + x)) = 8
(-8 + -1x + (8 * x + x * x)) = 8
(-8 + -1x + (8x + x2)) = 8

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

Solving
-8 + 7x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + -8 + 7x + x2 = 8 + -8

Combine like terms: -8 + -8 = -16
-16 + 7x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-16 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 7x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 7x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 7x + x2 = 0 + 16
7x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
7x + x2 = 16

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 16 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 16 + 12.25

Combine like terms: 16 + 12.25 = 28.25
12.25 + 7x + x2 = 28.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
x + 3.5 = 5.315072906

Simplifying
x + 3.5 = 5.315072906

Reorder the terms:
3.5 + x = 5.315072906

Solving
3.5 + x = 5.315072906

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 5.315072906 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.315072906 + -3.5
x = 5.315072906 + -3.5

Combine like terms: 5.315072906 + -3.5 = 1.815072906
x = 1.815072906

Simplifying
x = 1.815072906


Subproblem 2
x + 3.5 = -5.315072906

Simplifying
x + 3.5 = -5.315072906

Reorder the terms:
3.5 + x = -5.315072906

Solving
3.5 + x = -5.315072906

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -5.315072906 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.315072906 + -3.5
x = -5.315072906 + -3.5

Combine like terms: -5.315072906 + -3.5 = -8.815072906
x = -8.815072906

Simplifying
x = -8.815072906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.815072906, -8.815072906}

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