z^2+6z-25=0

Solution for z^2+6z-25=0 equation:

Simplifying
z2 + 6z + -25 = 0

Reorder the terms:
-25 + 6z + z2 = 0

Solving
-25 + 6z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 6z + 25 + z2 = 0 + 25

Reorder the terms:
-25 + 25 + 6z + z2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 6z + z2 = 0 + 25
6z + z2 = 0 + 25

Combine like terms: 0 + 25 = 25
6z + z2 = 25

The z term is 6z.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6z + 9 + z2 = 25 + 9

Reorder the terms:
9 + 6z + z2 = 25 + 9

Combine like terms: 25 + 9 = 34
9 + 6z + z2 = 34

Factor a perfect square on the left side:
(z + 3)(z + 3) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(z + 3) equal to 5.830951895 and -5.830951895.

Subproblem 1
z + 3 = 5.830951895

Simplifying
z + 3 = 5.830951895

Reorder the terms:
3 + z = 5.830951895

Solving
3 + z = 5.830951895

Solving for variable 'z'.

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

Add '-3' to each side of the equation.
3 + -3 + z = 5.830951895 + -3

Combine like terms: 3 + -3 = 0
0 + z = 5.830951895 + -3
z = 5.830951895 + -3

Combine like terms: 5.830951895 + -3 = 2.830951895
z = 2.830951895

Simplifying
z = 2.830951895

Subproblem 2
z + 3 = -5.830951895

Simplifying
z + 3 = -5.830951895

Reorder the terms:
3 + z = -5.830951895

Solving
3 + z = -5.830951895

Solving for variable 'z'.

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

Add '-3' to each side of the equation.
3 + -3 + z = -5.830951895 + -3

Combine like terms: 3 + -3 = 0
0 + z = -5.830951895 + -3
z = -5.830951895 + -3

Combine like terms: -5.830951895 + -3 = -8.830951895
z = -8.830951895

Simplifying
z = -8.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {2.830951895, -8.830951895}