8-x=(x+6)(x+6)

Solution for 8-x=(x+6)(x+6) equation:

Simplifying
8 + -1x = (x + 6)(x + 6)

Reorder the terms:
8 + -1x = (6 + x)(x + 6)

Reorder the terms:
8 + -1x = (6 + x)(6 + x)

Multiply (6 + x) * (6 + x)
8 + -1x = (6(6 + x) + x(6 + x))
8 + -1x = ((6 * 6 + x * 6) + x(6 + x))
8 + -1x = ((36 + 6x) + x(6 + x))
8 + -1x = (36 + 6x + (6 * x + x * x))
8 + -1x = (36 + 6x + (6x + x2))

Combine like terms: 6x + 6x = 12x
8 + -1x = (36 + 12x + x2)

Solving
8 + -1x = 36 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
8 + -36 + -1x + -12x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 8 + -36 = -28
-28 + -1x + -12x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: -1x + -12x = -13x
-28 + -13x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Reorder the terms:
-28 + -13x + -1x2 = 36 + -36 + 12x + -12x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-28 + -13x + -1x2 = 0 + 12x + -12x + x2 + -1x2
-28 + -13x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
-28 + -13x + -1x2 = 0 + x2 + -1x2
-28 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-28 + -13x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(28 + 13x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(28 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
28 + 13x + x2 = 0

Solving
28 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + 13x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + 13x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 13x + x2 = 0 + -28
13x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
13x + x2 = -28

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 = -28 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -28 + 42.25

Combine like terms: -28 + 42.25 = 14.25
42.25 + 13x + x2 = 14.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 6.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
x + 6.5 = 3.774917218

Simplifying
x + 6.5 = 3.774917218

Reorder the terms:
6.5 + x = 3.774917218

Solving
6.5 + x = 3.774917218

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 = 3.774917218 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 3.774917218 + -6.5
x = 3.774917218 + -6.5

Combine like terms: 3.774917218 + -6.5 = -2.725082782
x = -2.725082782

Simplifying
x = -2.725082782

Subproblem 2
x + 6.5 = -3.774917218

Simplifying
x + 6.5 = -3.774917218

Reorder the terms:
6.5 + x = -3.774917218

Solving
6.5 + x = -3.774917218

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 = -3.774917218 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -3.774917218 + -6.5
x = -3.774917218 + -6.5

Combine like terms: -3.774917218 + -6.5 = -10.274917218
x = -10.274917218

Simplifying
x = -10.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.725082782, -10.274917218}
Solution
x = {-2.725082782, -10.274917218}