0=x^2+x-0.02

Solution for 0=x^2+x-0.02 equation:

Simplifying
0 = x2 + x + -0.02

Reorder the terms:
0 = -0.02 + x + x2

Solving
0 = -0.02 + x + x2

Solving for variable 'x'.

Combine like terms: 0 + 0.02 = 0.02
0.02 + -1x + -1x2 = -0.02 + x + x2 + 0.02 + -1x + -1x2

Reorder the terms:
0.02 + -1x + -1x2 = -0.02 + 0.02 + x + -1x + x2 + -1x2

Combine like terms: -0.02 + 0.02 = 0.00
0.02 + -1x + -1x2 = 0.00 + x + -1x + x2 + -1x2
0.02 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
0.02 + -1x + -1x2 = 0 + x2 + -1x2
0.02 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.02 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.02 + x + x2 = 0

Move the constant term to the right:

Add '0.02' to each side of the equation.
-0.02 + x + 0.02 + x2 = 0 + 0.02

Reorder the terms:
-0.02 + 0.02 + x + x2 = 0 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + x + x2 = 0 + 0.02
x + x2 = 0 + 0.02

Combine like terms: 0 + 0.02 = 0.02
x + x2 = 0.02

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.
 + 0.25 + x2 = 0.02 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.02 + 0.25

Combine like terms: 0.02 + 0.25 = 0.27
1.25 + x2 = 0.27

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.27

Calculate the square root of the right side: 0.519615242

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.519615242 and -0.519615242.

Subproblem 1
x + 0.5 = 0.519615242

Simplifying
x + 0.5 = 0.519615242

Reorder the terms:
0.5 + x = 0.519615242

Solving
0.5 + x = 0.519615242

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 = 0.519615242 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.519615242 + -0.5
x = 0.519615242 + -0.5

Combine like terms: 0.519615242 + -0.5 = 0.019615242
x = 0.019615242

Simplifying
x = 0.019615242

Subproblem 2
x + 0.5 = -0.519615242

Simplifying
x + 0.5 = -0.519615242

Reorder the terms:
0.5 + x = -0.519615242

Solving
0.5 + x = -0.519615242

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 = -0.519615242 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.519615242 + -0.5
x = -0.519615242 + -0.5

Combine like terms: -0.519615242 + -0.5 = -1.019615242
x = -1.019615242

Simplifying
x = -1.019615242

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.019615242, -1.019615242}