z^2+9z-154=0

Solution for z^2+9z-154=0 equation:

Simplifying
z2 + 9z + -154 = 0

Reorder the terms:
-154 + 9z + z2 = 0

Solving
-154 + 9z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '154' to each side of the equation.
-154 + 9z + 154 + z2 = 0 + 154

Reorder the terms:
-154 + 154 + 9z + z2 = 0 + 154

Combine like terms: -154 + 154 = 0
0 + 9z + z2 = 0 + 154
9z + z2 = 0 + 154

Combine like terms: 0 + 154 = 154
9z + z2 = 154

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 = 154 + 20.25

Reorder the terms:
20.25 + 9z + z2 = 154 + 20.25

Combine like terms: 154 + 20.25 = 174.25
20.25 + 9z + z2 = 174.25

Factor a perfect square on the left side:
(z + 4.5)(z + 4.5) = 174.25

Calculate the square root of the right side: 13.200378782

Break this problem into two subproblems by setting 
(z + 4.5) equal to 13.200378782 and -13.200378782.

Subproblem 1
z + 4.5 = 13.200378782

Simplifying
z + 4.5 = 13.200378782

Reorder the terms:
4.5 + z = 13.200378782

Solving
4.5 + z = 13.200378782

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 = 13.200378782 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + z = 13.200378782 + -4.5
z = 13.200378782 + -4.5

Combine like terms: 13.200378782 + -4.5 = 8.700378782
z = 8.700378782

Simplifying
z = 8.700378782

Subproblem 2
z + 4.5 = -13.200378782

Simplifying
z + 4.5 = -13.200378782

Reorder the terms:
4.5 + z = -13.200378782

Solving
4.5 + z = -13.200378782

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 = -13.200378782 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + z = -13.200378782 + -4.5
z = -13.200378782 + -4.5

Combine like terms: -13.200378782 + -4.5 = -17.700378782
z = -17.700378782

Simplifying
z = -17.700378782

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {8.700378782, -17.700378782}