20x^2+22x+3=0

Solution for 20x^2+22x+3=0 equation:

Simplifying
20x2 + 22x + 3 = 0

Reorder the terms:
3 + 22x + 20x2 = 0

Solving
3 + 22x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
0.15 + 1.1x + x2 = 0

Move the constant term to the right:

Add '-0.15' to each side of the equation.
0.15 + 1.1x + -0.15 + x2 = 0 + -0.15

Reorder the terms:
0.15 + -0.15 + 1.1x + x2 = 0 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + 1.1x + x2 = 0 + -0.15
1.1x + x2 = 0 + -0.15

Combine like terms: 0 + -0.15 = -0.15
1.1x + x2 = -0.15

The x term is 1.1x.  Take half its coefficient (0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
1.1x + 0.3025 + x2 = -0.15 + 0.3025

Reorder the terms:
0.3025 + 1.1x + x2 = -0.15 + 0.3025

Combine like terms: -0.15 + 0.3025 = 0.1525
0.3025 + 1.1x + x2 = 0.1525

Factor a perfect square on the left side:
(x + 0.55)(x + 0.55) = 0.1525

Calculate the square root of the right side: 0.390512484

Break this problem into two subproblems by setting 
(x + 0.55) equal to 0.390512484 and -0.390512484.

Subproblem 1
x + 0.55 = 0.390512484

Simplifying
x + 0.55 = 0.390512484

Reorder the terms:
0.55 + x = 0.390512484

Solving
0.55 + x = 0.390512484

Solving for variable 'x'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + x = 0.390512484 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + x = 0.390512484 + -0.55
x = 0.390512484 + -0.55

Combine like terms: 0.390512484 + -0.55 = -0.159487516
x = -0.159487516

Simplifying
x = -0.159487516

Subproblem 2
x + 0.55 = -0.390512484

Simplifying
x + 0.55 = -0.390512484

Reorder the terms:
0.55 + x = -0.390512484

Solving
0.55 + x = -0.390512484

Solving for variable 'x'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + x = -0.390512484 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + x = -0.390512484 + -0.55
x = -0.390512484 + -0.55

Combine like terms: -0.390512484 + -0.55 = -0.940512484
x = -0.940512484

Simplifying
x = -0.940512484

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.159487516, -0.940512484}