z^2+16z+42=0

Solution for z^2+16z+42=0 equation:

Simplifying
z2 + 16z + 42 = 0

Reorder the terms:
42 + 16z + z2 = 0

Solving
42 + 16z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + 16z + -42 + z2 = 0 + -42

Reorder the terms:
42 + -42 + 16z + z2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 16z + z2 = 0 + -42
16z + z2 = 0 + -42

Combine like terms: 0 + -42 = -42
16z + z2 = -42

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 = -42 + 64

Reorder the terms:
64 + 16z + z2 = -42 + 64

Combine like terms: -42 + 64 = 22
64 + 16z + z2 = 22

Factor a perfect square on the left side:
(z + 8)(z + 8) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(z + 8) equal to 4.69041576 and -4.69041576.

Subproblem 1
z + 8 = 4.69041576

Simplifying
z + 8 = 4.69041576

Reorder the terms:
8 + z = 4.69041576

Solving
8 + z = 4.69041576

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 = 4.69041576 + -8

Combine like terms: 8 + -8 = 0
0 + z = 4.69041576 + -8
z = 4.69041576 + -8

Combine like terms: 4.69041576 + -8 = -3.30958424
z = -3.30958424

Simplifying
z = -3.30958424

Subproblem 2
z + 8 = -4.69041576

Simplifying
z + 8 = -4.69041576

Reorder the terms:
8 + z = -4.69041576

Solving
8 + z = -4.69041576

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 = -4.69041576 + -8

Combine like terms: 8 + -8 = 0
0 + z = -4.69041576 + -8
z = -4.69041576 + -8

Combine like terms: -4.69041576 + -8 = -12.69041576
z = -12.69041576

Simplifying
z = -12.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-3.30958424, -12.69041576}