3q^2+9q+3=0

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Solution for 3q^2+9q+3=0 equation: 


Simplifying
3q2 + 9q + 3 = 0

Reorder the terms:
3 + 9q + 3q2 = 0

Solving
3 + 9q + 3q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 3q + q2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + 3q + q2)' equal to zero and attempt to solve:

Simplifying
1 + 3q + q2 = 0

Solving
1 + 3q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3q + -1 + q2 = 0 + -1

Reorder the terms:
1 + -1 + 3q + q2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3q + q2 = 0 + -1
3q + q2 = 0 + -1

Combine like terms: 0 + -1 = -1
3q + q2 = -1

The q term is 3q.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3q + 2.25 + q2 = -1 + 2.25

Reorder the terms:
2.25 + 3q + q2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + 3q + q2 = 1.25

Factor a perfect square on the left side:
(q + 1.5)(q + 1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(q + 1.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
q + 1.5 = 1.118033989

Simplifying
q + 1.5 = 1.118033989

Reorder the terms:
1.5 + q = 1.118033989

Solving
1.5 + q = 1.118033989

Solving for variable 'q'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + q = 1.118033989 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + q = 1.118033989 + -1.5
q = 1.118033989 + -1.5

Combine like terms: 1.118033989 + -1.5 = -0.381966011
q = -0.381966011

Simplifying
q = -0.381966011


Subproblem 2
q + 1.5 = -1.118033989

Simplifying
q + 1.5 = -1.118033989

Reorder the terms:
1.5 + q = -1.118033989

Solving
1.5 + q = -1.118033989

Solving for variable 'q'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + q = -1.118033989 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + q = -1.118033989 + -1.5
q = -1.118033989 + -1.5

Combine like terms: -1.118033989 + -1.5 = -2.618033989
q = -2.618033989

Simplifying
q = -2.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-0.381966011, -2.618033989}
Solution
q = {-0.381966011, -2.618033989}

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