r+r^2=0.3075

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Solution for r+r^2=0.3075 equation: 


Simplifying
r + r2 = 0.3075

Solving
r + r2 = 0.3075

Solving for variable 'r'.

Reorder the terms:
-0.3075 + r + r2 = 0.3075 + -0.3075

Combine like terms: 0.3075 + -0.3075 = 0.0000
-0.3075 + r + r2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '0.3075' to each side of the equation.
-0.3075 + r + 0.3075 + r2 = 0.0000 + 0.3075

Reorder the terms:
-0.3075 + 0.3075 + r + r2 = 0.0000 + 0.3075

Combine like terms: -0.3075 + 0.3075 = 0.0000
0.0000 + r + r2 = 0.0000 + 0.3075
r + r2 = 0.0000 + 0.3075

Combine like terms: 0.0000 + 0.3075 = 0.3075
r + r2 = 0.3075

The r term is r.  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 = 0.3075 + 0.25

Reorder the terms:
0.25 + r + r2 = 0.3075 + 0.25

Combine like terms: 0.3075 + 0.25 = 0.5575
0.25 + r + r2 = 0.5575

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 0.5575

Calculate the square root of the right side: 0.746659226

Break this problem into two subproblems by setting 
(r + 0.5) equal to 0.746659226 and -0.746659226.


Subproblem 1
r + 0.5 = 0.746659226

Simplifying
r + 0.5 = 0.746659226

Reorder the terms:
0.5 + r = 0.746659226

Solving
0.5 + r = 0.746659226

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 = 0.746659226 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 0.746659226 + -0.5
r = 0.746659226 + -0.5

Combine like terms: 0.746659226 + -0.5 = 0.246659226
r = 0.246659226

Simplifying
r = 0.246659226


Subproblem 2
r + 0.5 = -0.746659226

Simplifying
r + 0.5 = -0.746659226

Reorder the terms:
0.5 + r = -0.746659226

Solving
0.5 + r = -0.746659226

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 = -0.746659226 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -0.746659226 + -0.5
r = -0.746659226 + -0.5

Combine like terms: -0.746659226 + -0.5 = -1.246659226
r = -1.246659226

Simplifying
r = -1.246659226


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.246659226, -1.246659226}

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