10x^2+20x+9=0

Solution for 10x^2+20x+9=0 equation:

Simplifying
10x2 + 20x + 9 = 0

Reorder the terms:
9 + 20x + 10x2 = 0

Solving
9 + 20x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
0.9 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.9' to each side of the equation.
0.9 + 2x + -0.9 + x2 = 0 + -0.9

Reorder the terms:
0.9 + -0.9 + 2x + x2 = 0 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + 2x + x2 = 0 + -0.9
2x + x2 = 0 + -0.9

Combine like terms: 0 + -0.9 = -0.9
2x + x2 = -0.9

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 = -0.9 + 1

Reorder the terms:
1 + 2x + x2 = -0.9 + 1

Combine like terms: -0.9 + 1 = 0.1
1 + 2x + x2 = 0.1

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.1

Calculate the square root of the right side: 0.316227766

Break this problem into two subproblems by setting 
(x + 1) equal to 0.316227766 and -0.316227766.

Subproblem 1
x + 1 = 0.316227766

Simplifying
x + 1 = 0.316227766

Reorder the terms:
1 + x = 0.316227766

Solving
1 + x = 0.316227766

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 = 0.316227766 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.316227766 + -1
x = 0.316227766 + -1

Combine like terms: 0.316227766 + -1 = -0.683772234
x = -0.683772234

Simplifying
x = -0.683772234

Subproblem 2
x + 1 = -0.316227766

Simplifying
x + 1 = -0.316227766

Reorder the terms:
1 + x = -0.316227766

Solving
1 + x = -0.316227766

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 = -0.316227766 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.316227766 + -1
x = -0.316227766 + -1

Combine like terms: -0.316227766 + -1 = -1.316227766
x = -1.316227766

Simplifying
x = -1.316227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.683772234, -1.316227766}