2r=5-4r^2

Solution for 2r=5-4r^2 equation:

Simplifying
2r = 5 + -4r2

Solving
2r = 5 + -4r2

Solving for variable 'r'.

Reorder the terms:
-5 + 2r + 4r2 = 5 + -4r2 + -5 + 4r2

Reorder the terms:
-5 + 2r + 4r2 = 5 + -5 + -4r2 + 4r2

Combine like terms: 5 + -5 = 0
-5 + 2r + 4r2 = 0 + -4r2 + 4r2
-5 + 2r + 4r2 = -4r2 + 4r2

Combine like terms: -4r2 + 4r2 = 0
-5 + 2r + 4r2 = 0

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

Divide each side by '4'.
-1.25 + 0.5r + r2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.5r + 1.25 + r2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.5r + r2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.5r + r2 = 0 + 1.25
0.5r + r2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.5r + r2 = 1.25

The r term is 0.5r.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5r + 0.0625 + r2 = 1.25 + 0.0625

Reorder the terms:
0.0625 + 0.5r + r2 = 1.25 + 0.0625

Combine like terms: 1.25 + 0.0625 = 1.3125
0.0625 + 0.5r + r2 = 1.3125

Factor a perfect square on the left side:
(r + 0.25)(r + 0.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(r + 0.25) equal to 1.145643924 and -1.145643924.

Subproblem 1
r + 0.25 = 1.145643924

Simplifying
r + 0.25 = 1.145643924

Reorder the terms:
0.25 + r = 1.145643924

Solving
0.25 + r = 1.145643924

Solving for variable 'r'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + r = 1.145643924 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + r = 1.145643924 + -0.25
r = 1.145643924 + -0.25

Combine like terms: 1.145643924 + -0.25 = 0.895643924
r = 0.895643924

Simplifying
r = 0.895643924

Subproblem 2
r + 0.25 = -1.145643924

Simplifying
r + 0.25 = -1.145643924

Reorder the terms:
0.25 + r = -1.145643924

Solving
0.25 + r = -1.145643924

Solving for variable 'r'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + r = -1.145643924 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + r = -1.145643924 + -0.25
r = -1.145643924 + -0.25

Combine like terms: -1.145643924 + -0.25 = -1.395643924
r = -1.395643924

Simplifying
r = -1.395643924

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.895643924, -1.395643924}