z^2+9z-20=0

Solution for z^2+9z-20=0 equation:

Simplifying
z2 + 9z + -20 = 0

Reorder the terms:
-20 + 9z + z2 = 0

Solving
-20 + 9z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 9z + 20 + z2 = 0 + 20

Reorder the terms:
-20 + 20 + 9z + z2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 9z + z2 = 0 + 20
9z + z2 = 0 + 20

Combine like terms: 0 + 20 = 20
9z + z2 = 20

The z term is 9z.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9z + 20.25 + z2 = 20 + 20.25

Reorder the terms:
20.25 + 9z + z2 = 20 + 20.25

Combine like terms: 20 + 20.25 = 40.25
20.25 + 9z + z2 = 40.25

Factor a perfect square on the left side:
(z + 4.5)(z + 4.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(z + 4.5) equal to 6.34428877 and -6.34428877.

Subproblem 1
z + 4.5 = 6.34428877

Simplifying
z + 4.5 = 6.34428877

Reorder the terms:
4.5 + z = 6.34428877

Solving
4.5 + z = 6.34428877

Solving for variable 'z'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + z = 6.34428877 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + z = 6.34428877 + -4.5
z = 6.34428877 + -4.5

Combine like terms: 6.34428877 + -4.5 = 1.84428877
z = 1.84428877

Simplifying
z = 1.84428877

Subproblem 2
z + 4.5 = -6.34428877

Simplifying
z + 4.5 = -6.34428877

Reorder the terms:
4.5 + z = -6.34428877

Solving
4.5 + z = -6.34428877

Solving for variable 'z'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + z = -6.34428877 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + z = -6.34428877 + -4.5
z = -6.34428877 + -4.5

Combine like terms: -6.34428877 + -4.5 = -10.84428877
z = -10.84428877

Simplifying
z = -10.84428877

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.84428877, -10.84428877}