(10x^2)+20x+2=0

Solution for (10x^2)+20x+2=0 equation:

Simplifying
(10x2) + 20x + 2 = 0

Reorder the terms:
2 + 20x + (10x2) = 0

Solving
2 + 20x + (10x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 10x + (5x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 10x + (5x2))' equal to zero and attempt to solve:

Simplifying
1 + 10x + (5x2) = 0

Solving
1 + 10x + (5x2) = 0

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

Divide each side by '5'.
0.2 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2x + x2 = 0 + -0.2
2x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2x + x2 = -0.2

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 = -0.2 + 1

Reorder the terms:
1 + 2x + x2 = -0.2 + 1

Combine like terms: -0.2 + 1 = 0.8
1 + 2x + x2 = 0.8

Factor a perfect square on the left side:
((x) + 1)((x) + 1) = 0.8

Calculate the square root of the right side: 0.894427191

Break this problem into two subproblems by setting 
((x) + 1) equal to 0.894427191 and -0.894427191.

Subproblem 1
(x) + 1 = 0.894427191

Simplifying
(x) + 1 = 0.894427191
x + 1 = 0.894427191

Reorder the terms:
1 + x = 0.894427191

Solving
1 + x = 0.894427191

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 = 0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.894427191 + -1
x = 0.894427191 + -1

Combine like terms: 0.894427191 + -1 = -0.105572809
x = -0.105572809

Simplifying
x = -0.105572809

Subproblem 2
(x) + 1 = -0.894427191

Simplifying
(x) + 1 = -0.894427191
x + 1 = -0.894427191

Reorder the terms:
1 + x = -0.894427191

Solving
1 + x = -0.894427191

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 = -0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.894427191 + -1
x = -0.894427191 + -1

Combine like terms: -0.894427191 + -1 = -1.894427191
x = -1.894427191

Simplifying
x = -1.894427191

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.105572809, -1.894427191}
Solution
x = {-0.105572809, -1.894427191}