0.01x-0.03=-0.1x^2

Solution for 0.01x-0.03=-0.1x^2 equation:

Simplifying
0.01x + -0.03 = -0.1x2

Reorder the terms:
-0.03 + 0.01x = -0.1x2

Solving
-0.03 + 0.01x = -0.1x2

Solving for variable 'x'.

Combine like terms: -0.1x2 + 0.1x2 = 0.0
-0.03 + 0.01x + 0.1x2 = 0.0

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

Divide each side by '0.1'.
-0.3 + 0.1x + x2 = 0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 0.1x + 0.3 + x2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 0.1x + x2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 0.1x + x2 = 0 + 0.3
0.1x + x2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
0.1x + x2 = 0.3

The x term is 0.1x.  Take half its coefficient (0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
0.1x + 0.0025 + x2 = 0.3 + 0.0025

Reorder the terms:
0.0025 + 0.1x + x2 = 0.3 + 0.0025

Combine like terms: 0.3 + 0.0025 = 0.3025
0.0025 + 0.1x + x2 = 0.3025

Factor a perfect square on the left side:
(x + 0.05)(x + 0.05) = 0.3025

Calculate the square root of the right side: 0.55

Break this problem into two subproblems by setting 
(x + 0.05) equal to 0.55 and -0.55.

Subproblem 1
x + 0.05 = 0.55

Simplifying
x + 0.05 = 0.55

Reorder the terms:
0.05 + x = 0.55

Solving
0.05 + x = 0.55

Solving for variable 'x'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + x = 0.55 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + x = 0.55 + -0.05
x = 0.55 + -0.05

Combine like terms: 0.55 + -0.05 = 0.5
x = 0.5

Simplifying
x = 0.5

Subproblem 2
x + 0.05 = -0.55

Simplifying
x + 0.05 = -0.55

Reorder the terms:
0.05 + x = -0.55

Solving
0.05 + x = -0.55

Solving for variable 'x'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + x = -0.55 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + x = -0.55 + -0.05
x = -0.55 + -0.05

Combine like terms: -0.55 + -0.05 = -0.6
x = -0.6

Simplifying
x = -0.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -0.6}