z^2+2z-26=0

Solution for z^2+2z-26=0 equation:

Simplifying
z2 + 2z + -26 = 0

Reorder the terms:
-26 + 2z + z2 = 0

Solving
-26 + 2z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 2z + 26 + z2 = 0 + 26

Reorder the terms:
-26 + 26 + 2z + z2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 2z + z2 = 0 + 26
2z + z2 = 0 + 26

Combine like terms: 0 + 26 = 26
2z + z2 = 26

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 = 26 + 1

Reorder the terms:
1 + 2z + z2 = 26 + 1

Combine like terms: 26 + 1 = 27
1 + 2z + z2 = 27

Factor a perfect square on the left side:
(z + 1)(z + 1) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(z + 1) equal to 5.196152423 and -5.196152423.

Subproblem 1
z + 1 = 5.196152423

Simplifying
z + 1 = 5.196152423

Reorder the terms:
1 + z = 5.196152423

Solving
1 + z = 5.196152423

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 = 5.196152423 + -1

Combine like terms: 1 + -1 = 0
0 + z = 5.196152423 + -1
z = 5.196152423 + -1

Combine like terms: 5.196152423 + -1 = 4.196152423
z = 4.196152423

Simplifying
z = 4.196152423

Subproblem 2
z + 1 = -5.196152423

Simplifying
z + 1 = -5.196152423

Reorder the terms:
1 + z = -5.196152423

Solving
1 + z = -5.196152423

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 = -5.196152423 + -1

Combine like terms: 1 + -1 = 0
0 + z = -5.196152423 + -1
z = -5.196152423 + -1

Combine like terms: -5.196152423 + -1 = -6.196152423
z = -6.196152423

Simplifying
z = -6.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {4.196152423, -6.196152423}