9x^2+x=-2

Solution for 9x^2+x=-2 equation:

Simplifying
9x2 + x = -2

Reorder the terms:
x + 9x2 = -2

Solving
x + 9x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + x + 9x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + x + 9x2 = 0

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

Divide each side by '9'.
0.2222222222 + 0.1111111111x + x2 = 0

Move the constant term to the right:

Add '-0.2222222222' to each side of the equation.
0.2222222222 + 0.1111111111x + -0.2222222222 + x2 = 0 + -0.2222222222

Reorder the terms:
0.2222222222 + -0.2222222222 + 0.1111111111x + x2 = 0 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + 0.1111111111x + x2 = 0 + -0.2222222222
0.1111111111x + x2 = 0 + -0.2222222222

Combine like terms: 0 + -0.2222222222 = -0.2222222222
0.1111111111x + x2 = -0.2222222222

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.
0.1111111111x + 0.25 + x2 = -0.2222222222 + 0.25

Reorder the terms:
0.25 + 0.1111111111x + x2 = -0.2222222222 + 0.25

Combine like terms: -0.2222222222 + 0.25 = 0.0277777778
0.25 + 0.1111111111x + x2 = 0.0277777778

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.0277777778

Calculate the square root of the right side: 0.166666667

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.166666667 and -0.166666667.

Subproblem 1
x + 0.5 = 0.166666667

Simplifying
x + 0.5 = 0.166666667

Reorder the terms:
0.5 + x = 0.166666667

Solving
0.5 + x = 0.166666667

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 = 0.166666667 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.166666667 + -0.5
x = 0.166666667 + -0.5

Combine like terms: 0.166666667 + -0.5 = -0.333333333
x = -0.333333333

Simplifying
x = -0.333333333

Subproblem 2
x + 0.5 = -0.166666667

Simplifying
x + 0.5 = -0.166666667

Reorder the terms:
0.5 + x = -0.166666667

Solving
0.5 + x = -0.166666667

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 = -0.166666667 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.166666667 + -0.5
x = -0.166666667 + -0.5

Combine like terms: -0.166666667 + -0.5 = -0.666666667
x = -0.666666667

Simplifying
x = -0.666666667

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.333333333, -0.666666667}