16=28r-r^2

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Solution for 16=28r-r^2 equation: 


Simplifying
16 = 28r + -1r2

Solving
16 = 28r + -1r2

Solving for variable 'r'.

Reorder the terms:
16 + -28r + r2 = 28r + -28r + -1r2 + r2

Combine like terms: 28r + -28r = 0
16 + -28r + r2 = 0 + -1r2 + r2
16 + -28r + r2 = -1r2 + r2

Combine like terms: -1r2 + r2 = 0
16 + -28r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -28r + -16 + r2 = 0 + -16

Reorder the terms:
16 + -16 + -28r + r2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -28r + r2 = 0 + -16
-28r + r2 = 0 + -16

Combine like terms: 0 + -16 = -16
-28r + r2 = -16

The r term is -28r.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28r + 196 + r2 = -16 + 196

Reorder the terms:
196 + -28r + r2 = -16 + 196

Combine like terms: -16 + 196 = 180
196 + -28r + r2 = 180

Factor a perfect square on the left side:
(r + -14)(r + -14) = 180

Calculate the square root of the right side: 13.416407865

Break this problem into two subproblems by setting 
(r + -14) equal to 13.416407865 and -13.416407865.


Subproblem 1
r + -14 = 13.416407865

Simplifying
r + -14 = 13.416407865

Reorder the terms:
-14 + r = 13.416407865

Solving
-14 + r = 13.416407865

Solving for variable 'r'.

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

Add '14' to each side of the equation.
-14 + 14 + r = 13.416407865 + 14

Combine like terms: -14 + 14 = 0
0 + r = 13.416407865 + 14
r = 13.416407865 + 14

Combine like terms: 13.416407865 + 14 = 27.416407865
r = 27.416407865

Simplifying
r = 27.416407865


Subproblem 2
r + -14 = -13.416407865

Simplifying
r + -14 = -13.416407865

Reorder the terms:
-14 + r = -13.416407865

Solving
-14 + r = -13.416407865

Solving for variable 'r'.

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

Add '14' to each side of the equation.
-14 + 14 + r = -13.416407865 + 14

Combine like terms: -14 + 14 = 0
0 + r = -13.416407865 + 14
r = -13.416407865 + 14

Combine like terms: -13.416407865 + 14 = 0.583592135
r = 0.583592135

Simplifying
r = 0.583592135


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {27.416407865, 0.583592135}

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