0.04r-0.02+0.16r^2=0

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Solution for 0.04r-0.02+0.16r^2=0 equation: 


Simplifying
0.04r + -0.02 + 0.16r2 = 0

Reorder the terms:
-0.02 + 0.04r + 0.16r2 = 0

Solving
-0.02 + 0.04r + 0.16r2 = 0

Solving for variable 'r'.

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

Divide each side by '0.16'.
-0.125 + 0.25r + r2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.25r + 0.125 + r2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.25r + r2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.25r + r2 = 0 + 0.125
0.25r + r2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.25r + r2 = 0.125

The r term is 0.25r.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25r + 0.015625 + r2 = 0.125 + 0.015625

Reorder the terms:
0.015625 + 0.25r + r2 = 0.125 + 0.015625

Combine like terms: 0.125 + 0.015625 = 0.140625
0.015625 + 0.25r + r2 = 0.140625

Factor a perfect square on the left side:
(r + 0.125)(r + 0.125) = 0.140625

Calculate the square root of the right side: 0.375

Break this problem into two subproblems by setting 
(r + 0.125) equal to 0.375 and -0.375.


Subproblem 1
r + 0.125 = 0.375

Simplifying
r + 0.125 = 0.375

Reorder the terms:
0.125 + r = 0.375

Solving
0.125 + r = 0.375

Solving for variable 'r'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + r = 0.375 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + r = 0.375 + -0.125
r = 0.375 + -0.125

Combine like terms: 0.375 + -0.125 = 0.25
r = 0.25

Simplifying
r = 0.25


Subproblem 2
r + 0.125 = -0.375

Simplifying
r + 0.125 = -0.375

Reorder the terms:
0.125 + r = -0.375

Solving
0.125 + r = -0.375

Solving for variable 'r'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + r = -0.375 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + r = -0.375 + -0.125
r = -0.375 + -0.125

Combine like terms: -0.375 + -0.125 = -0.5
r = -0.5

Simplifying
r = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.25, -0.5}

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