r(r+1)-0.3=0

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Solution for r(r+1)-0.3=0 equation: 


Simplifying
r(r + 1) + -0.3 = 0

Reorder the terms:
r(1 + r) + -0.3 = 0
(1 * r + r * r) + -0.3 = 0
(1r + r2) + -0.3 = 0

Reorder the terms:
-0.3 + 1r + r2 = 0

Solving
-0.3 + 1r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 1r + 0.3 + r2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 1r + r2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 1r + r2 = 0 + 0.3
1r + r2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
1r + r2 = 0.3

The r term is 1r.  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.
r + 0.25 + r2 = 0.3 + 0.25

Reorder the terms:
0.25 + r + r2 = 0.3 + 0.25

Combine like terms: 0.3 + 0.25 = 0.55
0.25 + r + r2 = 0.55

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 0.55

Calculate the square root of the right side: 0.741619849

Break this problem into two subproblems by setting 
(r + 0.5) equal to 0.741619849 and -0.741619849.


Subproblem 1
r + 0.5 = 0.741619849

Simplifying
r + 0.5 = 0.741619849

Reorder the terms:
0.5 + r = 0.741619849

Solving
0.5 + r = 0.741619849

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 0.741619849 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 0.741619849 + -0.5
r = 0.741619849 + -0.5

Combine like terms: 0.741619849 + -0.5 = 0.241619849
r = 0.241619849

Simplifying
r = 0.241619849


Subproblem 2
r + 0.5 = -0.741619849

Simplifying
r + 0.5 = -0.741619849

Reorder the terms:
0.5 + r = -0.741619849

Solving
0.5 + r = -0.741619849

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -0.741619849 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -0.741619849 + -0.5
r = -0.741619849 + -0.5

Combine like terms: -0.741619849 + -0.5 = -1.241619849
r = -1.241619849

Simplifying
r = -1.241619849


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.241619849, -1.241619849}

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