9x^2+38x+3=0

Solution for 9x^2+38x+3=0 equation:

Simplifying
9x2 + 38x + 3 = 0

Reorder the terms:
3 + 38x + 9x2 = 0

Solving
3 + 38x + 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'.
0.3333333333 + 4.222222222x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 4.222222222x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 4.222222222x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 4.222222222x + x2 = 0 + -0.3333333333
4.222222222x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
4.222222222x + x2 = -0.3333333333

The x term is 4.222222222x.  Take half its coefficient (2.111111111).
Square it (4.456790123) and add it to both sides.

Add '4.456790123' to each side of the equation.
4.222222222x + 4.456790123 + x2 = -0.3333333333 + 4.456790123

Reorder the terms:
4.456790123 + 4.222222222x + x2 = -0.3333333333 + 4.456790123

Combine like terms: -0.3333333333 + 4.456790123 = 4.1234567897
4.456790123 + 4.222222222x + x2 = 4.1234567897

Factor a perfect square on the left side:
(x + 2.111111111)(x + 2.111111111) = 4.1234567897

Calculate the square root of the right side: 2.030629654

Break this problem into two subproblems by setting 
(x + 2.111111111) equal to 2.030629654 and -2.030629654.

Subproblem 1
x + 2.111111111 = 2.030629654

Simplifying
x + 2.111111111 = 2.030629654

Reorder the terms:
2.111111111 + x = 2.030629654

Solving
2.111111111 + x = 2.030629654

Solving for variable 'x'.

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

Add '-2.111111111' to each side of the equation.
2.111111111 + -2.111111111 + x = 2.030629654 + -2.111111111

Combine like terms: 2.111111111 + -2.111111111 = 0.000000000
0.000000000 + x = 2.030629654 + -2.111111111
x = 2.030629654 + -2.111111111

Combine like terms: 2.030629654 + -2.111111111 = -0.080481457
x = -0.080481457

Simplifying
x = -0.080481457

Subproblem 2
x + 2.111111111 = -2.030629654

Simplifying
x + 2.111111111 = -2.030629654

Reorder the terms:
2.111111111 + x = -2.030629654

Solving
2.111111111 + x = -2.030629654

Solving for variable 'x'.

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

Add '-2.111111111' to each side of the equation.
2.111111111 + -2.111111111 + x = -2.030629654 + -2.111111111

Combine like terms: 2.111111111 + -2.111111111 = 0.000000000
0.000000000 + x = -2.030629654 + -2.111111111
x = -2.030629654 + -2.111111111

Combine like terms: -2.030629654 + -2.111111111 = -4.141740765
x = -4.141740765

Simplifying
x = -4.141740765

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.080481457, -4.141740765}