8x=8-2x(x+2)

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Solution for 8x=8-2x(x+2) equation: 


Simplifying
8x = 8 + -2x(x + 2)

Reorder the terms:
8x = 8 + -2x(2 + x)
8x = 8 + (2 * -2x + x * -2x)
8x = 8 + (-4x + -2x2)

Solving
8x = 8 + -4x + -2x2

Solving for variable 'x'.

Reorder the terms:
-8 + 8x + 4x + 2x2 = 8 + -4x + -2x2 + -8 + 4x + 2x2

Combine like terms: 8x + 4x = 12x
-8 + 12x + 2x2 = 8 + -4x + -2x2 + -8 + 4x + 2x2

Reorder the terms:
-8 + 12x + 2x2 = 8 + -8 + -4x + 4x + -2x2 + 2x2

Combine like terms: 8 + -8 = 0
-8 + 12x + 2x2 = 0 + -4x + 4x + -2x2 + 2x2
-8 + 12x + 2x2 = -4x + 4x + -2x2 + 2x2

Combine like terms: -4x + 4x = 0
-8 + 12x + 2x2 = 0 + -2x2 + 2x2
-8 + 12x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-8 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + 6x + x2 = 0

Solving
-4 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 6x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6x + x2 = 0 + 4
6x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
6x + x2 = 4

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 4 + 9

Reorder the terms:
9 + 6x + x2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + 6x + x2 = 13

Factor a perfect square on the left side:
(x + 3)(x + 3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 3) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + 3 = 3.605551275

Simplifying
x + 3 = 3.605551275

Reorder the terms:
3 + x = 3.605551275

Solving
3 + x = 3.605551275

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.605551275 + -3
x = 3.605551275 + -3

Combine like terms: 3.605551275 + -3 = 0.605551275
x = 0.605551275

Simplifying
x = 0.605551275


Subproblem 2
x + 3 = -3.605551275

Simplifying
x + 3 = -3.605551275

Reorder the terms:
3 + x = -3.605551275

Solving
3 + x = -3.605551275

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.605551275 + -3
x = -3.605551275 + -3

Combine like terms: -3.605551275 + -3 = -6.605551275
x = -6.605551275

Simplifying
x = -6.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.605551275, -6.605551275}
Solution
x = {0.605551275, -6.605551275}

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