z^2+9z-26=0

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Solution for z^2+9z-26=0 equation: 


Simplifying
z2 + 9z + -26 = 0

Reorder the terms:
-26 + 9z + z2 = 0

Solving
-26 + 9z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 9z + 26 + z2 = 0 + 26

Reorder the terms:
-26 + 26 + 9z + z2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 9z + z2 = 0 + 26
9z + z2 = 0 + 26

Combine like terms: 0 + 26 = 26
9z + z2 = 26

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 = 26 + 20.25

Reorder the terms:
20.25 + 9z + z2 = 26 + 20.25

Combine like terms: 26 + 20.25 = 46.25
20.25 + 9z + z2 = 46.25

Factor a perfect square on the left side:
(z + 4.5)(z + 4.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(z + 4.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
z + 4.5 = 6.800735254

Simplifying
z + 4.5 = 6.800735254

Reorder the terms:
4.5 + z = 6.800735254

Solving
4.5 + z = 6.800735254

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 = 6.800735254 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + z = 6.800735254 + -4.5
z = 6.800735254 + -4.5

Combine like terms: 6.800735254 + -4.5 = 2.300735254
z = 2.300735254

Simplifying
z = 2.300735254


Subproblem 2
z + 4.5 = -6.800735254

Simplifying
z + 4.5 = -6.800735254

Reorder the terms:
4.5 + z = -6.800735254

Solving
4.5 + z = -6.800735254

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 = -6.800735254 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + z = -6.800735254 + -4.5
z = -6.800735254 + -4.5

Combine like terms: -6.800735254 + -4.5 = -11.300735254
z = -11.300735254

Simplifying
z = -11.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {2.300735254, -11.300735254}

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