x^2+x+0.09=0

Solution for x^2+x+0.09=0 equation:

Simplifying
x2 + x + 0.09 = 0

Reorder the terms:
0.09 + x + x2 = 0

Solving
0.09 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.09' to each side of the equation.
0.09 + x + -0.09 + x2 = 0 + -0.09

Reorder the terms:
0.09 + -0.09 + x + x2 = 0 + -0.09

Combine like terms: 0.09 + -0.09 = 0.00
0.00 + x + x2 = 0 + -0.09
x + x2 = 0 + -0.09

Combine like terms: 0 + -0.09 = -0.09
x + x2 = -0.09

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -0.09 + 0.25

Reorder the terms:
0.25 + x + x2 = -0.09 + 0.25

Combine like terms: -0.09 + 0.25 = 0.16
0.25 + x + x2 = 0.16

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.16

Calculate the square root of the right side: 0.4

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.4 and -0.4.

Subproblem 1
x + 0.5 = 0.4

Simplifying
x + 0.5 = 0.4

Reorder the terms:
0.5 + x = 0.4

Solving
0.5 + x = 0.4

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.4 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.4 + -0.5
x = 0.4 + -0.5

Combine like terms: 0.4 + -0.5 = -0.1
x = -0.1

Simplifying
x = -0.1

Subproblem 2
x + 0.5 = -0.4

Simplifying
x + 0.5 = -0.4

Reorder the terms:
0.5 + x = -0.4

Solving
0.5 + x = -0.4

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.4 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.4 + -0.5
x = -0.4 + -0.5

Combine like terms: -0.4 + -0.5 = -0.9
x = -0.9

Simplifying
x = -0.9

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1, -0.9}