1114.386=2*3.14*r^2+2*3.14*r*6.5

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Solution for 1114.386=2*3.14*r^2+2*3.14*r*6.5 equation: 


Simplifying
1114.386 = 2 * 3.14r2 + 2 * 3.14r * 6.5

Multiply 2 * 3.14
1114.386 = 6.28r2 + 2 * 3.14r * 6.5

Reorder the terms for easier multiplication:
1114.386 = 6.28r2 + 2 * 3.14 * 6.5r

Multiply 2 * 3.14
1114.386 = 6.28r2 + 6.28 * 6.5r

Multiply 6.28 * 6.5
1114.386 = 6.28r2 + 40.82r

Reorder the terms:
1114.386 = 40.82r + 6.28r2

Solving
1114.386 = 40.82r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
1114.386 + -40.82r + -6.28r2 = 40.82r + -40.82r + 6.28r2 + -6.28r2

Combine like terms: 40.82r + -40.82r = 0.00
1114.386 + -40.82r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
1114.386 + -40.82r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
1114.386 + -40.82r + -6.28r2 = 0.00

Begin completing the square.  Divide all terms by
-6.28 the coefficient of the squared term: 

Divide each side by '-6.28'.
-177.45 + 6.5r + r2 = 0

Move the constant term to the right:

Add '177.45' to each side of the equation.
-177.45 + 6.5r + 177.45 + r2 = 0 + 177.45

Reorder the terms:
-177.45 + 177.45 + 6.5r + r2 = 0 + 177.45

Combine like terms: -177.45 + 177.45 = 0.00
0.00 + 6.5r + r2 = 0 + 177.45
6.5r + r2 = 0 + 177.45

Combine like terms: 0 + 177.45 = 177.45
6.5r + r2 = 177.45

The r term is 6.5r.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5r + 10.5625 + r2 = 177.45 + 10.5625

Reorder the terms:
10.5625 + 6.5r + r2 = 177.45 + 10.5625

Combine like terms: 177.45 + 10.5625 = 188.0125
10.5625 + 6.5r + r2 = 188.0125

Factor a perfect square on the left side:
(r + 3.25)(r + 3.25) = 188.0125

Calculate the square root of the right side: 13.711765021

Break this problem into two subproblems by setting 
(r + 3.25) equal to 13.711765021 and -13.711765021.


Subproblem 1
r + 3.25 = 13.711765021

Simplifying
r + 3.25 = 13.711765021

Reorder the terms:
3.25 + r = 13.711765021

Solving
3.25 + r = 13.711765021

Solving for variable 'r'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + r = 13.711765021 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + r = 13.711765021 + -3.25
r = 13.711765021 + -3.25

Combine like terms: 13.711765021 + -3.25 = 10.461765021
r = 10.461765021

Simplifying
r = 10.461765021


Subproblem 2
r + 3.25 = -13.711765021

Simplifying
r + 3.25 = -13.711765021

Reorder the terms:
3.25 + r = -13.711765021

Solving
3.25 + r = -13.711765021

Solving for variable 'r'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + r = -13.711765021 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + r = -13.711765021 + -3.25
r = -13.711765021 + -3.25

Combine like terms: -13.711765021 + -3.25 = -16.961765021
r = -16.961765021

Simplifying
r = -16.961765021


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {10.461765021, -16.961765021}

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