r^2+.6r-.4=0

Solution for r^2+.6r-.4=0 equation:

Simplifying
r2 + 0.6r + -0.4 = 0

Reorder the terms:
-0.4 + 0.6r + r2 = 0

Solving
-0.4 + 0.6r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.6r + 0.4 + r2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.6r + r2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.6r + r2 = 0 + 0.4
0.6r + r2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.6r + r2 = 0.4

The r term is 0.6r.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6r + 0.09 + r2 = 0.4 + 0.09

Reorder the terms:
0.09 + 0.6r + r2 = 0.4 + 0.09

Combine like terms: 0.4 + 0.09 = 0.49
0.09 + 0.6r + r2 = 0.49

Factor a perfect square on the left side:
(r + 0.3)(r + 0.3) = 0.49

Calculate the square root of the right side: 0.7

Break this problem into two subproblems by setting 
(r + 0.3) equal to 0.7 and -0.7.

Subproblem 1
r + 0.3 = 0.7

Simplifying
r + 0.3 = 0.7

Reorder the terms:
0.3 + r = 0.7

Solving
0.3 + r = 0.7

Solving for variable 'r'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + r = 0.7 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + r = 0.7 + -0.3
r = 0.7 + -0.3

Combine like terms: 0.7 + -0.3 = 0.4
r = 0.4

Simplifying
r = 0.4

Subproblem 2
r + 0.3 = -0.7

Simplifying
r + 0.3 = -0.7

Reorder the terms:
0.3 + r = -0.7

Solving
0.3 + r = -0.7

Solving for variable 'r'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + r = -0.7 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + r = -0.7 + -0.3
r = -0.7 + -0.3

Combine like terms: -0.7 + -0.3 = -1
r = -1

Simplifying
r = -1

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.4, -1}