25.748=2*3.14*r^2+2*3.14*r*13

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Solution for 25.748=2*3.14*r^2+2*3.14*r*13 equation: 


Simplifying
25.748 = 2 * 3.14r2 + 2 * 3.14r * 13

Multiply 2 * 3.14
25.748 = 6.28r2 + 2 * 3.14r * 13

Reorder the terms for easier multiplication:
25.748 = 6.28r2 + 2 * 3.14 * 13r

Multiply 2 * 3.14
25.748 = 6.28r2 + 6.28 * 13r

Multiply 6.28 * 13
25.748 = 6.28r2 + 81.64r

Reorder the terms:
25.748 = 81.64r + 6.28r2

Solving
25.748 = 81.64r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
25.748 + -81.64r + -6.28r2 = 81.64r + -81.64r + 6.28r2 + -6.28r2

Combine like terms: 81.64r + -81.64r = 0.00
25.748 + -81.64r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
25.748 + -81.64r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
25.748 + -81.64r + -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'.
-4.1 + 13r + r2 = 0

Move the constant term to the right:

Add '4.1' to each side of the equation.
-4.1 + 13r + 4.1 + r2 = 0 + 4.1

Reorder the terms:
-4.1 + 4.1 + 13r + r2 = 0 + 4.1

Combine like terms: -4.1 + 4.1 = 0.0
0.0 + 13r + r2 = 0 + 4.1
13r + r2 = 0 + 4.1

Combine like terms: 0 + 4.1 = 4.1
13r + r2 = 4.1

The r term is 13r.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13r + 42.25 + r2 = 4.1 + 42.25

Reorder the terms:
42.25 + 13r + r2 = 4.1 + 42.25

Combine like terms: 4.1 + 42.25 = 46.35
42.25 + 13r + r2 = 46.35

Factor a perfect square on the left side:
(r + 6.5)(r + 6.5) = 46.35

Calculate the square root of the right side: 6.808083431

Break this problem into two subproblems by setting 
(r + 6.5) equal to 6.808083431 and -6.808083431.


Subproblem 1
r + 6.5 = 6.808083431

Simplifying
r + 6.5 = 6.808083431

Reorder the terms:
6.5 + r = 6.808083431

Solving
6.5 + r = 6.808083431

Solving for variable 'r'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + r = 6.808083431 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + r = 6.808083431 + -6.5
r = 6.808083431 + -6.5

Combine like terms: 6.808083431 + -6.5 = 0.308083431
r = 0.308083431

Simplifying
r = 0.308083431


Subproblem 2
r + 6.5 = -6.808083431

Simplifying
r + 6.5 = -6.808083431

Reorder the terms:
6.5 + r = -6.808083431

Solving
6.5 + r = -6.808083431

Solving for variable 'r'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + r = -6.808083431 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + r = -6.808083431 + -6.5
r = -6.808083431 + -6.5

Combine like terms: -6.808083431 + -6.5 = -13.308083431
r = -13.308083431

Simplifying
r = -13.308083431


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.308083431, -13.308083431}

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