z^2+16z+44=0

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Solution for z^2+16z+44=0 equation: 


Simplifying
z2 + 16z + 44 = 0

Reorder the terms:
44 + 16z + z2 = 0

Solving
44 + 16z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + 16z + -44 + z2 = 0 + -44

Reorder the terms:
44 + -44 + 16z + z2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + 16z + z2 = 0 + -44
16z + z2 = 0 + -44

Combine like terms: 0 + -44 = -44
16z + z2 = -44

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 = -44 + 64

Reorder the terms:
64 + 16z + z2 = -44 + 64

Combine like terms: -44 + 64 = 20
64 + 16z + z2 = 20

Factor a perfect square on the left side:
(z + 8)(z + 8) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(z + 8) equal to 4.472135955 and -4.472135955.


Subproblem 1
z + 8 = 4.472135955

Simplifying
z + 8 = 4.472135955

Reorder the terms:
8 + z = 4.472135955

Solving
8 + z = 4.472135955

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 = 4.472135955 + -8

Combine like terms: 8 + -8 = 0
0 + z = 4.472135955 + -8
z = 4.472135955 + -8

Combine like terms: 4.472135955 + -8 = -3.527864045
z = -3.527864045

Simplifying
z = -3.527864045


Subproblem 2
z + 8 = -4.472135955

Simplifying
z + 8 = -4.472135955

Reorder the terms:
8 + z = -4.472135955

Solving
8 + z = -4.472135955

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 = -4.472135955 + -8

Combine like terms: 8 + -8 = 0
0 + z = -4.472135955 + -8
z = -4.472135955 + -8

Combine like terms: -4.472135955 + -8 = -12.472135955
z = -12.472135955

Simplifying
z = -12.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-3.527864045, -12.472135955}

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