9x^2+45x+6=0

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Solution for 9x^2+45x+6=0 equation: 


Simplifying
9x2 + 45x + 6 = 0

Reorder the terms:
6 + 45x + 9x2 = 0

Solving
6 + 45x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 15x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + 15x + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + 15x + 3x2 = 0

Solving
2 + 15x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
0.6666666667 + 5x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 5x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 5x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 5x + x2 = 0 + -0.6666666667
5x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
5x + x2 = -0.6666666667

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -0.6666666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -0.6666666667 + 6.25

Combine like terms: -0.6666666667 + 6.25 = 5.5833333333
6.25 + 5x + x2 = 5.5833333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 5.5833333333

Calculate the square root of the right side: 2.362907813

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.362907813 and -2.362907813.


Subproblem 1
x + 2.5 = 2.362907813

Simplifying
x + 2.5 = 2.362907813

Reorder the terms:
2.5 + x = 2.362907813

Solving
2.5 + x = 2.362907813

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.362907813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.362907813 + -2.5
x = 2.362907813 + -2.5

Combine like terms: 2.362907813 + -2.5 = -0.137092187
x = -0.137092187

Simplifying
x = -0.137092187


Subproblem 2
x + 2.5 = -2.362907813

Simplifying
x + 2.5 = -2.362907813

Reorder the terms:
2.5 + x = -2.362907813

Solving
2.5 + x = -2.362907813

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.362907813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.362907813 + -2.5
x = -2.362907813 + -2.5

Combine like terms: -2.362907813 + -2.5 = -4.862907813
x = -4.862907813

Simplifying
x = -4.862907813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.137092187, -4.862907813}
Solution
x = {-0.137092187, -4.862907813}

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