19x^2+38x+1=0

Solution for 19x^2+38x+1=0 equation:

Simplifying
19x2 + 38x + 1 = 0

Reorder the terms:
1 + 38x + 19x2 = 0

Solving
1 + 38x + 19x2 = 0

Solving for variable 'x'.

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

Divide each side by '19'.
0.05263157895 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.05263157895' to each side of the equation.
0.05263157895 + 2x + -0.05263157895 + x2 = 0 + -0.05263157895

Reorder the terms:
0.05263157895 + -0.05263157895 + 2x + x2 = 0 + -0.05263157895

Combine like terms: 0.05263157895 + -0.05263157895 = 0.00000000000
0.00000000000 + 2x + x2 = 0 + -0.05263157895
2x + x2 = 0 + -0.05263157895

Combine like terms: 0 + -0.05263157895 = -0.05263157895
2x + x2 = -0.05263157895

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.05263157895 + 1

Reorder the terms:
1 + 2x + x2 = -0.05263157895 + 1

Combine like terms: -0.05263157895 + 1 = 0.94736842105
1 + 2x + x2 = 0.94736842105

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.94736842105

Calculate the square root of the right side: 0.973328527

Break this problem into two subproblems by setting 
(x + 1) equal to 0.973328527 and -0.973328527.

Subproblem 1
x + 1 = 0.973328527

Simplifying
x + 1 = 0.973328527

Reorder the terms:
1 + x = 0.973328527

Solving
1 + x = 0.973328527

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 0.973328527 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.973328527 + -1
x = 0.973328527 + -1

Combine like terms: 0.973328527 + -1 = -0.026671473
x = -0.026671473

Simplifying
x = -0.026671473

Subproblem 2
x + 1 = -0.973328527

Simplifying
x + 1 = -0.973328527

Reorder the terms:
1 + x = -0.973328527

Solving
1 + x = -0.973328527

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -0.973328527 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.973328527 + -1
x = -0.973328527 + -1

Combine like terms: -0.973328527 + -1 = -1.973328527
x = -1.973328527

Simplifying
x = -1.973328527

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.026671473, -1.973328527}