3x^2+30x+1=0

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Solution for 3x^2+30x+1=0 equation: 


Simplifying
3x2 + 30x + 1 = 0

Reorder the terms:
1 + 30x + 3x2 = 0

Solving
1 + 30x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
0.3333333333 + 10x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 10x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 10x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 10x + x2 = 0 + -0.3333333333
10x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
10x + x2 = -0.3333333333

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -0.3333333333 + 25

Reorder the terms:
25 + 10x + x2 = -0.3333333333 + 25

Combine like terms: -0.3333333333 + 25 = 24.6666666667
25 + 10x + x2 = 24.6666666667

Factor a perfect square on the left side:
(x + 5)(x + 5) = 24.6666666667

Calculate the square root of the right side: 4.966554809

Break this problem into two subproblems by setting 
(x + 5) equal to 4.966554809 and -4.966554809.


Subproblem 1
x + 5 = 4.966554809

Simplifying
x + 5 = 4.966554809

Reorder the terms:
5 + x = 4.966554809

Solving
5 + x = 4.966554809

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 4.966554809 + -5

Combine like terms: 5 + -5 = 0
0 + x = 4.966554809 + -5
x = 4.966554809 + -5

Combine like terms: 4.966554809 + -5 = -0.033445191
x = -0.033445191

Simplifying
x = -0.033445191


Subproblem 2
x + 5 = -4.966554809

Simplifying
x + 5 = -4.966554809

Reorder the terms:
5 + x = -4.966554809

Solving
5 + x = -4.966554809

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -4.966554809 + -5

Combine like terms: 5 + -5 = 0
0 + x = -4.966554809 + -5
x = -4.966554809 + -5

Combine like terms: -4.966554809 + -5 = -9.966554809
x = -9.966554809

Simplifying
x = -9.966554809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.033445191, -9.966554809}

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