0=9x^2+41x+3

Solution for 0=9x^2+41x+3 equation:

Simplifying
0 = 9x2 + 41x + 3

Reorder the terms:
0 = 3 + 41x + 9x2

Solving
0 = 3 + 41x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -3 = -3
-3 + -41x + -9x2 = 3 + 41x + 9x2 + -3 + -41x + -9x2

Reorder the terms:
-3 + -41x + -9x2 = 3 + -3 + 41x + -41x + 9x2 + -9x2

Combine like terms: 3 + -3 = 0
-3 + -41x + -9x2 = 0 + 41x + -41x + 9x2 + -9x2
-3 + -41x + -9x2 = 41x + -41x + 9x2 + -9x2

Combine like terms: 41x + -41x = 0
-3 + -41x + -9x2 = 0 + 9x2 + -9x2
-3 + -41x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-3 + -41x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 41x + 9x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 41x + 9x2)' equal to zero and attempt to solve:

Simplifying
3 + 41x + 9x2 = 0

Solving
3 + 41x + 9x2 = 0

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

Divide each side by '9'.
0.3333333333 + 4.555555556x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 4.555555556x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 4.555555556x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 4.555555556x + x2 = 0 + -0.3333333333
4.555555556x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
4.555555556x + x2 = -0.3333333333

The x term is 4.555555556x.  Take half its coefficient (2.277777778).
Square it (5.188271606) and add it to both sides.

Add '5.188271606' to each side of the equation.
4.555555556x + 5.188271606 + x2 = -0.3333333333 + 5.188271606

Reorder the terms:
5.188271606 + 4.555555556x + x2 = -0.3333333333 + 5.188271606

Combine like terms: -0.3333333333 + 5.188271606 = 4.8549382727
5.188271606 + 4.555555556x + x2 = 4.8549382727

Factor a perfect square on the left side:
(x + 2.277777778)(x + 2.277777778) = 4.8549382727

Calculate the square root of the right side: 2.203392446

Break this problem into two subproblems by setting 
(x + 2.277777778) equal to 2.203392446 and -2.203392446.

Subproblem 1
x + 2.277777778 = 2.203392446

Simplifying
x + 2.277777778 = 2.203392446

Reorder the terms:
2.277777778 + x = 2.203392446

Solving
2.277777778 + x = 2.203392446

Solving for variable 'x'.

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

Add '-2.277777778' to each side of the equation.
2.277777778 + -2.277777778 + x = 2.203392446 + -2.277777778

Combine like terms: 2.277777778 + -2.277777778 = 0.000000000
0.000000000 + x = 2.203392446 + -2.277777778
x = 2.203392446 + -2.277777778

Combine like terms: 2.203392446 + -2.277777778 = -0.074385332
x = -0.074385332

Simplifying
x = -0.074385332

Subproblem 2
x + 2.277777778 = -2.203392446

Simplifying
x + 2.277777778 = -2.203392446

Reorder the terms:
2.277777778 + x = -2.203392446

Solving
2.277777778 + x = -2.203392446

Solving for variable 'x'.

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

Add '-2.277777778' to each side of the equation.
2.277777778 + -2.277777778 + x = -2.203392446 + -2.277777778

Combine like terms: 2.277777778 + -2.277777778 = 0.000000000
0.000000000 + x = -2.203392446 + -2.277777778
x = -2.203392446 + -2.277777778

Combine like terms: -2.203392446 + -2.277777778 = -4.481170224
x = -4.481170224

Simplifying
x = -4.481170224

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.074385332, -4.481170224}
Solution
x = {-0.074385332, -4.481170224}