q^2+9q+9=0

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Solution for q^2+9q+9=0 equation: 


Simplifying
q2 + 9q + 9 = 0

Reorder the terms:
9 + 9q + q2 = 0

Solving
9 + 9q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 9q + -9 + q2 = 0 + -9

Reorder the terms:
9 + -9 + 9q + q2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 9q + q2 = 0 + -9
9q + q2 = 0 + -9

Combine like terms: 0 + -9 = -9
9q + q2 = -9

The q term is 9q.  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.
9q + 20.25 + q2 = -9 + 20.25

Reorder the terms:
20.25 + 9q + q2 = -9 + 20.25

Combine like terms: -9 + 20.25 = 11.25
20.25 + 9q + q2 = 11.25

Factor a perfect square on the left side:
(q + 4.5)(q + 4.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(q + 4.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
q + 4.5 = 3.354101966

Simplifying
q + 4.5 = 3.354101966

Reorder the terms:
4.5 + q = 3.354101966

Solving
4.5 + q = 3.354101966

Solving for variable 'q'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + q = 3.354101966 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + q = 3.354101966 + -4.5
q = 3.354101966 + -4.5

Combine like terms: 3.354101966 + -4.5 = -1.145898034
q = -1.145898034

Simplifying
q = -1.145898034


Subproblem 2
q + 4.5 = -3.354101966

Simplifying
q + 4.5 = -3.354101966

Reorder the terms:
4.5 + q = -3.354101966

Solving
4.5 + q = -3.354101966

Solving for variable 'q'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + q = -3.354101966 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + q = -3.354101966 + -4.5
q = -3.354101966 + -4.5

Combine like terms: -3.354101966 + -4.5 = -7.854101966
q = -7.854101966

Simplifying
q = -7.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-1.145898034, -7.854101966}

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