9x^2+30x+1=0

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Solution for 9x^2+30x+1=0 equation: 


Simplifying
9x2 + 30x + 1 = 0

Reorder the terms:
1 + 30x + 9x2 = 0

Solving
1 + 30x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
0.1111111111 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + 3.333333333x + -0.1111111111 + x2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + 3.333333333x + x2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + 3.333333333x + x2 = 0 + -0.1111111111
3.333333333x + x2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
3.333333333x + x2 = -0.1111111111

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = -0.1111111111 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -0.1111111111 + 2.777777779

Combine like terms: -0.1111111111 + 2.777777779 = 2.6666666679
2.777777779 + 3.333333333x + x2 = 2.6666666679

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 2.6666666679

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 1.632993162 and -1.632993162.


Subproblem 1
x + 1.666666667 = 1.632993162

Simplifying
x + 1.666666667 = 1.632993162

Reorder the terms:
1.666666667 + x = 1.632993162

Solving
1.666666667 + x = 1.632993162

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 1.632993162 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 1.632993162 + -1.666666667
x = 1.632993162 + -1.666666667

Combine like terms: 1.632993162 + -1.666666667 = -0.033673505
x = -0.033673505

Simplifying
x = -0.033673505


Subproblem 2
x + 1.666666667 = -1.632993162

Simplifying
x + 1.666666667 = -1.632993162

Reorder the terms:
1.666666667 + x = -1.632993162

Solving
1.666666667 + x = -1.632993162

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -1.632993162 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -1.632993162 + -1.666666667
x = -1.632993162 + -1.666666667

Combine like terms: -1.632993162 + -1.666666667 = -3.299659829
x = -3.299659829

Simplifying
x = -3.299659829


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.033673505, -3.299659829}

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