0=x^2+16x+8

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Solution for 0=x^2+16x+8 equation: 


Simplifying
0 = x2 + 16x + 8

Reorder the terms:
0 = 8 + 16x + x2

Solving
0 = 8 + 16x + x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -16x + -1x2 = 8 + 16x + x2 + -8 + -16x + -1x2

Reorder the terms:
-8 + -16x + -1x2 = 8 + -8 + 16x + -16x + x2 + -1x2

Combine like terms: 8 + -8 = 0
-8 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2
-8 + -16x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
-8 + -16x + -1x2 = 0 + x2 + -1x2
-8 + -16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -16x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 16x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
8 + 16x + x2 = 0

Solving
8 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 16x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 16x + x2 = 0 + -8

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

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

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -8 + 64

Reorder the terms:
64 + 16x + x2 = -8 + 64

Combine like terms: -8 + 64 = 56
64 + 16x + x2 = 56

Factor a perfect square on the left side:
(x + 8)(x + 8) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + 8) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + 8 = 7.483314774

Simplifying
x + 8 = 7.483314774

Reorder the terms:
8 + x = 7.483314774

Solving
8 + x = 7.483314774

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 7.483314774 + -8

Combine like terms: 8 + -8 = 0
0 + x = 7.483314774 + -8
x = 7.483314774 + -8

Combine like terms: 7.483314774 + -8 = -0.516685226
x = -0.516685226

Simplifying
x = -0.516685226


Subproblem 2
x + 8 = -7.483314774

Simplifying
x + 8 = -7.483314774

Reorder the terms:
8 + x = -7.483314774

Solving
8 + x = -7.483314774

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -7.483314774 + -8

Combine like terms: 8 + -8 = 0
0 + x = -7.483314774 + -8
x = -7.483314774 + -8

Combine like terms: -7.483314774 + -8 = -15.483314774
x = -15.483314774

Simplifying
x = -15.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.516685226, -15.483314774}
Solution
x = {-0.516685226, -15.483314774}

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