s^2+9s-9=0

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Solution for s^2+9s-9=0 equation: 


Simplifying
s2 + 9s + -9 = 0

Reorder the terms:
-9 + 9s + s2 = 0

Solving
-9 + 9s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 9s + 9 + s2 = 0 + 9

Reorder the terms:
-9 + 9 + 9s + s2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 9s + s2 = 0 + 9
9s + s2 = 0 + 9

Combine like terms: 0 + 9 = 9
9s + s2 = 9

The s term is 9s.  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.
9s + 20.25 + s2 = 9 + 20.25

Reorder the terms:
20.25 + 9s + s2 = 9 + 20.25

Combine like terms: 9 + 20.25 = 29.25
20.25 + 9s + s2 = 29.25

Factor a perfect square on the left side:
(s + 4.5)(s + 4.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(s + 4.5) equal to 5.408326913 and -5.408326913.


Subproblem 1
s + 4.5 = 5.408326913

Simplifying
s + 4.5 = 5.408326913

Reorder the terms:
4.5 + s = 5.408326913

Solving
4.5 + s = 5.408326913

Solving for variable 's'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + s = 5.408326913 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + s = 5.408326913 + -4.5
s = 5.408326913 + -4.5

Combine like terms: 5.408326913 + -4.5 = 0.908326913
s = 0.908326913

Simplifying
s = 0.908326913


Subproblem 2
s + 4.5 = -5.408326913

Simplifying
s + 4.5 = -5.408326913

Reorder the terms:
4.5 + s = -5.408326913

Solving
4.5 + s = -5.408326913

Solving for variable 's'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + s = -5.408326913 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + s = -5.408326913 + -4.5
s = -5.408326913 + -4.5

Combine like terms: -5.408326913 + -4.5 = -9.908326913
s = -9.908326913

Simplifying
s = -9.908326913


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.908326913, -9.908326913}

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