5r^2=73-r

Solution for 5r^2=73-r equation:

Simplifying
5r2 = 73 + -1r

Solving
5r2 = 73 + -1r

Solving for variable 'r'.

Reorder the terms:
-73 + r + 5r2 = 73 + -1r + -73 + r

Reorder the terms:
-73 + r + 5r2 = 73 + -73 + -1r + r

Combine like terms: 73 + -73 = 0
-73 + r + 5r2 = 0 + -1r + r
-73 + r + 5r2 = -1r + r

Combine like terms: -1r + r = 0
-73 + r + 5r2 = 0

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

Divide each side by '5'.
-14.6 + 0.2r + r2 = 0

Move the constant term to the right:

Add '14.6' to each side of the equation.
-14.6 + 0.2r + 14.6 + r2 = 0 + 14.6

Reorder the terms:
-14.6 + 14.6 + 0.2r + r2 = 0 + 14.6

Combine like terms: -14.6 + 14.6 = 0.0
0.0 + 0.2r + r2 = 0 + 14.6
0.2r + r2 = 0 + 14.6

Combine like terms: 0 + 14.6 = 14.6
0.2r + r2 = 14.6

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.
0.2r + 0.25 + r2 = 14.6 + 0.25

Reorder the terms:
0.25 + 0.2r + r2 = 14.6 + 0.25

Combine like terms: 14.6 + 0.25 = 14.85
0.25 + 0.2r + r2 = 14.85

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 14.85

Calculate the square root of the right side: 3.853569774

Break this problem into two subproblems by setting 
(r + 0.5) equal to 3.853569774 and -3.853569774.

Subproblem 1
r + 0.5 = 3.853569774

Simplifying
r + 0.5 = 3.853569774

Reorder the terms:
0.5 + r = 3.853569774

Solving
0.5 + r = 3.853569774

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 = 3.853569774 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 3.853569774 + -0.5
r = 3.853569774 + -0.5

Combine like terms: 3.853569774 + -0.5 = 3.353569774
r = 3.353569774

Simplifying
r = 3.353569774

Subproblem 2
r + 0.5 = -3.853569774

Simplifying
r + 0.5 = -3.853569774

Reorder the terms:
0.5 + r = -3.853569774

Solving
0.5 + r = -3.853569774

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 = -3.853569774 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -3.853569774 + -0.5
r = -3.853569774 + -0.5

Combine like terms: -3.853569774 + -0.5 = -4.353569774
r = -4.353569774

Simplifying
r = -4.353569774

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.353569774, -4.353569774}