z^2+2z-4=0

Solution for z^2+2z-4=0 equation:

Simplifying
z2 + 2z + -4 = 0

Reorder the terms:
-4 + 2z + z2 = 0

Solving
-4 + 2z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2z + 4 + z2 = 0 + 4

Reorder the terms:
-4 + 4 + 2z + z2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2z + z2 = 0 + 4
2z + z2 = 0 + 4

Combine like terms: 0 + 4 = 4
2z + z2 = 4

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 = 4 + 1

Reorder the terms:
1 + 2z + z2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + 2z + z2 = 5

Factor a perfect square on the left side:
(z + 1)(z + 1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(z + 1) equal to 2.236067978 and -2.236067978.

Subproblem 1
z + 1 = 2.236067978

Simplifying
z + 1 = 2.236067978

Reorder the terms:
1 + z = 2.236067978

Solving
1 + z = 2.236067978

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 = 2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + z = 2.236067978 + -1
z = 2.236067978 + -1

Combine like terms: 2.236067978 + -1 = 1.236067978
z = 1.236067978

Simplifying
z = 1.236067978

Subproblem 2
z + 1 = -2.236067978

Simplifying
z + 1 = -2.236067978

Reorder the terms:
1 + z = -2.236067978

Solving
1 + z = -2.236067978

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 = -2.236067978 + -1

Combine like terms: 1 + -1 = 0
0 + z = -2.236067978 + -1
z = -2.236067978 + -1

Combine like terms: -2.236067978 + -1 = -3.236067978
z = -3.236067978

Simplifying
z = -3.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.236067978, -3.236067978}