z^2+2z-16=0

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

Simplifying
z2 + 2z + -16 = 0

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

Solving
-16 + 2z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The z term is 2z.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2z + 1 + z2 = 16 + 1

Reorder the terms:
1 + 2z + z2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + 2z + z2 = 17

Factor a perfect square on the left side:
(z + 1)(z + 1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(z + 1) equal to 4.123105626 and -4.123105626.

Subproblem 1
z + 1 = 4.123105626

Simplifying
z + 1 = 4.123105626

Reorder the terms:
1 + z = 4.123105626

Solving
1 + z = 4.123105626

Solving for variable 'z'.

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

Add '-1' to each side of the equation.
1 + -1 + z = 4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + z = 4.123105626 + -1
z = 4.123105626 + -1

Combine like terms: 4.123105626 + -1 = 3.123105626
z = 3.123105626

Simplifying
z = 3.123105626

Subproblem 2
z + 1 = -4.123105626

Simplifying
z + 1 = -4.123105626

Reorder the terms:
1 + z = -4.123105626

Solving
1 + z = -4.123105626

Solving for variable 'z'.

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

Add '-1' to each side of the equation.
1 + -1 + z = -4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + z = -4.123105626 + -1
z = -4.123105626 + -1

Combine like terms: -4.123105626 + -1 = -5.123105626
z = -5.123105626

Simplifying
z = -5.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {3.123105626, -5.123105626}