22x^2+x+2=0

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

Simplifying
22x2 + x + 2 = 0

Reorder the terms:
2 + x + 22x2 = 0

Solving
2 + x + 22x2 = 0

Solving for variable 'x'.

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

Divide each side by '22'.
0.09090909091 + 0.04545454545x + x2 = 0

Move the constant term to the right:

Add '-0.09090909091' to each side of the equation.
0.09090909091 + 0.04545454545x + -0.09090909091 + x2 = 0 + -0.09090909091

Reorder the terms:
0.09090909091 + -0.09090909091 + 0.04545454545x + x2 = 0 + -0.09090909091

Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000
0.00000000000 + 0.04545454545x + x2 = 0 + -0.09090909091
0.04545454545x + x2 = 0 + -0.09090909091

Combine like terms: 0 + -0.09090909091 = -0.09090909091
0.04545454545x + x2 = -0.09090909091

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.
0.04545454545x + 0.25 + x2 = -0.09090909091 + 0.25

Reorder the terms:
0.25 + 0.04545454545x + x2 = -0.09090909091 + 0.25

Combine like terms: -0.09090909091 + 0.25 = 0.15909090909
0.25 + 0.04545454545x + x2 = 0.15909090909

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.15909090909

Calculate the square root of the right side: 0.398862018

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.398862018 and -0.398862018.

Subproblem 1
x + 0.5 = 0.398862018

Simplifying
x + 0.5 = 0.398862018

Reorder the terms:
0.5 + x = 0.398862018

Solving
0.5 + x = 0.398862018

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 = 0.398862018 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.398862018 + -0.5
x = 0.398862018 + -0.5

Combine like terms: 0.398862018 + -0.5 = -0.101137982
x = -0.101137982

Simplifying
x = -0.101137982

Subproblem 2
x + 0.5 = -0.398862018

Simplifying
x + 0.5 = -0.398862018

Reorder the terms:
0.5 + x = -0.398862018

Solving
0.5 + x = -0.398862018

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 = -0.398862018 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.398862018 + -0.5
x = -0.398862018 + -0.5

Combine like terms: -0.398862018 + -0.5 = -0.898862018
x = -0.898862018

Simplifying
x = -0.898862018

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.101137982, -0.898862018}