9z^2-9z-9=0

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

Simplifying
9z2 + -9z + -9 = 0

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

Solving
-9 + -9z + 9z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-1 + -1z + z2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-1 + -1z + z2)' equal to zero and attempt to solve:

Simplifying
-1 + -1z + z2 = 0

Solving
-1 + -1z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1z + 1 + z2 = 0 + 1

Reorder the terms:
-1 + 1 + -1z + z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1z + z2 = 0 + 1
-1z + z2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1z + z2 = 1

The z term is -1z.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z + 0.25 + z2 = 1 + 0.25

Reorder the terms:
0.25 + -1z + z2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1z + z2 = 1.25

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(z + -0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
z + -0.5 = 1.118033989

Simplifying
z + -0.5 = 1.118033989

Reorder the terms:
-0.5 + z = 1.118033989

Solving
-0.5 + z = 1.118033989

Solving for variable 'z'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + z = 1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + z = 1.118033989 + 0.5
z = 1.118033989 + 0.5

Combine like terms: 1.118033989 + 0.5 = 1.618033989
z = 1.618033989

Simplifying
z = 1.618033989

Subproblem 2
z + -0.5 = -1.118033989

Simplifying
z + -0.5 = -1.118033989

Reorder the terms:
-0.5 + z = -1.118033989

Solving
-0.5 + z = -1.118033989

Solving for variable 'z'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + z = -1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + z = -1.118033989 + 0.5
z = -1.118033989 + 0.5

Combine like terms: -1.118033989 + 0.5 = -0.618033989
z = -0.618033989

Simplifying
z = -0.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.618033989, -0.618033989}
Solution
z = {1.618033989, -0.618033989}