z^2+16z+2=0

Solution for z^2+16z+2=0 equation:

Simplifying
z2 + 16z + 2 = 0

Reorder the terms:
2 + 16z + z2 = 0

Solving
2 + 16z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 16z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + 16z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 16z + z2 = 0 + -2
16z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
16z + z2 = -2

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

Add '64' to each side of the equation.
16z + 64 + z2 = -2 + 64

Reorder the terms:
64 + 16z + z2 = -2 + 64

Combine like terms: -2 + 64 = 62
64 + 16z + z2 = 62

Factor a perfect square on the left side:
(z + 8)(z + 8) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(z + 8) equal to 7.874007874 and -7.874007874.

Subproblem 1
z + 8 = 7.874007874

Simplifying
z + 8 = 7.874007874

Reorder the terms:
8 + z = 7.874007874

Solving
8 + z = 7.874007874

Solving for variable 'z'.

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

Add '-8' to each side of the equation.
8 + -8 + z = 7.874007874 + -8

Combine like terms: 8 + -8 = 0
0 + z = 7.874007874 + -8
z = 7.874007874 + -8

Combine like terms: 7.874007874 + -8 = -0.125992126
z = -0.125992126

Simplifying
z = -0.125992126

Subproblem 2
z + 8 = -7.874007874

Simplifying
z + 8 = -7.874007874

Reorder the terms:
8 + z = -7.874007874

Solving
8 + z = -7.874007874

Solving for variable 'z'.

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

Add '-8' to each side of the equation.
8 + -8 + z = -7.874007874 + -8

Combine like terms: 8 + -8 = 0
0 + z = -7.874007874 + -8
z = -7.874007874 + -8

Combine like terms: -7.874007874 + -8 = -15.874007874
z = -15.874007874

Simplifying
z = -15.874007874

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-0.125992126, -15.874007874}