16=38r-r^2

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Solution for 16=38r-r^2 equation: 


Simplifying
16 = 38r + -1r2

Solving
16 = 38r + -1r2

Solving for variable 'r'.

Reorder the terms:
16 + -38r + r2 = 38r + -38r + -1r2 + r2

Combine like terms: 38r + -38r = 0
16 + -38r + r2 = 0 + -1r2 + r2
16 + -38r + r2 = -1r2 + r2

Combine like terms: -1r2 + r2 = 0
16 + -38r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -38r + -16 + r2 = 0 + -16

Reorder the terms:
16 + -16 + -38r + r2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -38r + r2 = 0 + -16
-38r + r2 = 0 + -16

Combine like terms: 0 + -16 = -16
-38r + r2 = -16

The r term is -38r.  Take half its coefficient (-19).
Square it (361) and add it to both sides.

Add '361' to each side of the equation.
-38r + 361 + r2 = -16 + 361

Reorder the terms:
361 + -38r + r2 = -16 + 361

Combine like terms: -16 + 361 = 345
361 + -38r + r2 = 345

Factor a perfect square on the left side:
(r + -19)(r + -19) = 345

Calculate the square root of the right side: 18.574175621

Break this problem into two subproblems by setting 
(r + -19) equal to 18.574175621 and -18.574175621.


Subproblem 1
r + -19 = 18.574175621

Simplifying
r + -19 = 18.574175621

Reorder the terms:
-19 + r = 18.574175621

Solving
-19 + r = 18.574175621

Solving for variable 'r'.

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

Add '19' to each side of the equation.
-19 + 19 + r = 18.574175621 + 19

Combine like terms: -19 + 19 = 0
0 + r = 18.574175621 + 19
r = 18.574175621 + 19

Combine like terms: 18.574175621 + 19 = 37.574175621
r = 37.574175621

Simplifying
r = 37.574175621


Subproblem 2
r + -19 = -18.574175621

Simplifying
r + -19 = -18.574175621

Reorder the terms:
-19 + r = -18.574175621

Solving
-19 + r = -18.574175621

Solving for variable 'r'.

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

Add '19' to each side of the equation.
-19 + 19 + r = -18.574175621 + 19

Combine like terms: -19 + 19 = 0
0 + r = -18.574175621 + 19
r = -18.574175621 + 19

Combine like terms: -18.574175621 + 19 = 0.425824379
r = 0.425824379

Simplifying
r = 0.425824379


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {37.574175621, 0.425824379}

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