x^2+16x+5=0

Solution for x^2+16x+5=0 equation:

Simplifying
x2 + 16x + 5 = 0

Reorder the terms:
5 + 16x + x2 = 0

Solving
5 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 16x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 16x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 16x + x2 = 0 + -5
16x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
16x + x2 = -5

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 = -5 + 64

Reorder the terms:
64 + 16x + x2 = -5 + 64

Combine like terms: -5 + 64 = 59
64 + 16x + x2 = 59

Factor a perfect square on the left side:
(x + 8)(x + 8) = 59

Calculate the square root of the right side: 7.681145748

Break this problem into two subproblems by setting 
(x + 8) equal to 7.681145748 and -7.681145748.

Subproblem 1
x + 8 = 7.681145748

Simplifying
x + 8 = 7.681145748

Reorder the terms:
8 + x = 7.681145748

Solving
8 + x = 7.681145748

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 = 7.681145748 + -8

Combine like terms: 8 + -8 = 0
0 + x = 7.681145748 + -8
x = 7.681145748 + -8

Combine like terms: 7.681145748 + -8 = -0.318854252
x = -0.318854252

Simplifying
x = -0.318854252

Subproblem 2
x + 8 = -7.681145748

Simplifying
x + 8 = -7.681145748

Reorder the terms:
8 + x = -7.681145748

Solving
8 + x = -7.681145748

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 = -7.681145748 + -8

Combine like terms: 8 + -8 = 0
0 + x = -7.681145748 + -8
x = -7.681145748 + -8

Combine like terms: -7.681145748 + -8 = -15.681145748
x = -15.681145748

Simplifying
x = -15.681145748

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.318854252, -15.681145748}