r^2+0.25r=0.5

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Solution for r^2+0.25r=0.5 equation: 


Simplifying
r2 + 0.25r = 0.5

Reorder the terms:
0.25r + r2 = 0.5

Solving
0.25r + r2 = 0.5

Solving for variable 'r'.

Reorder the terms:
-0.5 + 0.25r + r2 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-0.5 + 0.25r + r2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.25r + 0.5 + r2 = 0.0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.25r + r2 = 0.0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.25r + r2 = 0.0 + 0.5
0.25r + r2 = 0.0 + 0.5

Combine like terms: 0.0 + 0.5 = 0.5
0.25r + r2 = 0.5

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 = 0.5 + 0.015625

Reorder the terms:
0.015625 + 0.25r + r2 = 0.5 + 0.015625

Combine like terms: 0.5 + 0.015625 = 0.515625
0.015625 + 0.25r + r2 = 0.515625

Factor a perfect square on the left side:
(r + 0.125)(r + 0.125) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(r + 0.125) equal to 0.718070331 and -0.718070331.


Subproblem 1
r + 0.125 = 0.718070331

Simplifying
r + 0.125 = 0.718070331

Reorder the terms:
0.125 + r = 0.718070331

Solving
0.125 + r = 0.718070331

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 = 0.718070331 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + r = 0.718070331 + -0.125
r = 0.718070331 + -0.125

Combine like terms: 0.718070331 + -0.125 = 0.593070331
r = 0.593070331

Simplifying
r = 0.593070331


Subproblem 2
r + 0.125 = -0.718070331

Simplifying
r + 0.125 = -0.718070331

Reorder the terms:
0.125 + r = -0.718070331

Solving
0.125 + r = -0.718070331

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 = -0.718070331 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + r = -0.718070331 + -0.125
r = -0.718070331 + -0.125

Combine like terms: -0.718070331 + -0.125 = -0.843070331
r = -0.843070331

Simplifying
r = -0.843070331


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.593070331, -0.843070331}

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