z^2-2z-9=0

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

Simplifying
z2 + -2z + -9 = 0

Reorder the terms:
-9 + -2z + z2 = 0

Solving
-9 + -2z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2z + 9 + z2 = 0 + 9

Reorder the terms:
-9 + 9 + -2z + z2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2z + z2 = 0 + 9
-2z + z2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2z + z2 = 9

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 = 9 + 1

Reorder the terms:
1 + -2z + z2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + -2z + z2 = 10

Factor a perfect square on the left side:
(z + -1)(z + -1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(z + -1) equal to 3.16227766 and -3.16227766.

Subproblem 1
z + -1 = 3.16227766

Simplifying
z + -1 = 3.16227766

Reorder the terms:
-1 + z = 3.16227766

Solving
-1 + z = 3.16227766

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 = 3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + z = 3.16227766 + 1
z = 3.16227766 + 1

Combine like terms: 3.16227766 + 1 = 4.16227766
z = 4.16227766

Simplifying
z = 4.16227766

Subproblem 2
z + -1 = -3.16227766

Simplifying
z + -1 = -3.16227766

Reorder the terms:
-1 + z = -3.16227766

Solving
-1 + z = -3.16227766

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 = -3.16227766 + 1

Combine like terms: -1 + 1 = 0
0 + z = -3.16227766 + 1
z = -3.16227766 + 1

Combine like terms: -3.16227766 + 1 = -2.16227766
z = -2.16227766

Simplifying
z = -2.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {4.16227766, -2.16227766}