z^2+8z-13=0

Solution for z^2+8z-13=0 equation:

Simplifying
z2 + 8z + -13 = 0

Reorder the terms:
-13 + 8z + z2 = 0

Solving
-13 + 8z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 8z + 13 + z2 = 0 + 13

Reorder the terms:
-13 + 13 + 8z + z2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 8z + z2 = 0 + 13
8z + z2 = 0 + 13

Combine like terms: 0 + 13 = 13
8z + z2 = 13

The z term is 8z.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8z + 16 + z2 = 13 + 16

Reorder the terms:
16 + 8z + z2 = 13 + 16

Combine like terms: 13 + 16 = 29
16 + 8z + z2 = 29

Factor a perfect square on the left side:
(z + 4)(z + 4) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(z + 4) equal to 5.385164807 and -5.385164807.

Subproblem 1
z + 4 = 5.385164807

Simplifying
z + 4 = 5.385164807

Reorder the terms:
4 + z = 5.385164807

Solving
4 + z = 5.385164807

Solving for variable 'z'.

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

Add '-4' to each side of the equation.
4 + -4 + z = 5.385164807 + -4

Combine like terms: 4 + -4 = 0
0 + z = 5.385164807 + -4
z = 5.385164807 + -4

Combine like terms: 5.385164807 + -4 = 1.385164807
z = 1.385164807

Simplifying
z = 1.385164807

Subproblem 2
z + 4 = -5.385164807

Simplifying
z + 4 = -5.385164807

Reorder the terms:
4 + z = -5.385164807

Solving
4 + z = -5.385164807

Solving for variable 'z'.

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

Add '-4' to each side of the equation.
4 + -4 + z = -5.385164807 + -4

Combine like terms: 4 + -4 = 0
0 + z = -5.385164807 + -4
z = -5.385164807 + -4

Combine like terms: -5.385164807 + -4 = -9.385164807
z = -9.385164807

Simplifying
z = -9.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.385164807, -9.385164807}