0=x^2+8x+8

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Solution for 0=x^2+8x+8 equation: 


Simplifying
0 = x2 + 8x + 8

Reorder the terms:
0 = 8 + 8x + x2

Solving
0 = 8 + 8x + x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -8x + -1x2 = 8 + 8x + x2 + -8 + -8x + -1x2

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

Combine like terms: 8 + -8 = 0
-8 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2
-8 + -8x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-8 + -8x + -1x2 = 0 + x2 + -1x2
-8 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 8x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
8 + 8x + x2 = 0

Solving
8 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 8x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 8x + x2 = 0 + -8

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

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

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -8 + 16

Reorder the terms:
16 + 8x + x2 = -8 + 16

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

Factor a perfect square on the left side:
(x + 4)(x + 4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 4) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + 4 = 2.828427125

Simplifying
x + 4 = 2.828427125

Reorder the terms:
4 + x = 2.828427125

Solving
4 + x = 2.828427125

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + x = 2.828427125 + -4
x = 2.828427125 + -4

Combine like terms: 2.828427125 + -4 = -1.171572875
x = -1.171572875

Simplifying
x = -1.171572875


Subproblem 2
x + 4 = -2.828427125

Simplifying
x + 4 = -2.828427125

Reorder the terms:
4 + x = -2.828427125

Solving
4 + x = -2.828427125

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + x = -2.828427125 + -4
x = -2.828427125 + -4

Combine like terms: -2.828427125 + -4 = -6.828427125
x = -6.828427125

Simplifying
x = -6.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.171572875, -6.828427125}
Solution
x = {-1.171572875, -6.828427125}

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