0=6.28r^2+1130.4r-14469.12

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Solution for 0=6.28r^2+1130.4r-14469.12 equation: 


Simplifying
0 = 6.28r2 + 1130.4r + -14469.12

Reorder the terms:
0 = -14469.12 + 1130.4r + 6.28r2

Solving
0 = -14469.12 + 1130.4r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 14469.12 = 14469.12
14469.12 + -1130.4r + -6.28r2 = -14469.12 + 1130.4r + 6.28r2 + 14469.12 + -1130.4r + -6.28r2

Reorder the terms:
14469.12 + -1130.4r + -6.28r2 = -14469.12 + 14469.12 + 1130.4r + -1130.4r + 6.28r2 + -6.28r2

Combine like terms: -14469.12 + 14469.12 = 0.00
14469.12 + -1130.4r + -6.28r2 = 0.00 + 1130.4r + -1130.4r + 6.28r2 + -6.28r2
14469.12 + -1130.4r + -6.28r2 = 1130.4r + -1130.4r + 6.28r2 + -6.28r2

Combine like terms: 1130.4r + -1130.4r = 0.0
14469.12 + -1130.4r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
14469.12 + -1130.4r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
14469.12 + -1130.4r + -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'.
-2304 + 180r + r2 = 0

Move the constant term to the right:

Add '2304' to each side of the equation.
-2304 + 180r + 2304 + r2 = 0 + 2304

Reorder the terms:
-2304 + 2304 + 180r + r2 = 0 + 2304

Combine like terms: -2304 + 2304 = 0
0 + 180r + r2 = 0 + 2304
180r + r2 = 0 + 2304

Combine like terms: 0 + 2304 = 2304
180r + r2 = 2304

The r term is 180r.  Take half its coefficient (90).
Square it (8100) and add it to both sides.

Add '8100' to each side of the equation.
180r + 8100 + r2 = 2304 + 8100

Reorder the terms:
8100 + 180r + r2 = 2304 + 8100

Combine like terms: 2304 + 8100 = 10404
8100 + 180r + r2 = 10404

Factor a perfect square on the left side:
(r + 90)(r + 90) = 10404

Calculate the square root of the right side: 102

Break this problem into two subproblems by setting 
(r + 90) equal to 102 and -102.


Subproblem 1
r + 90 = 102

Simplifying
r + 90 = 102

Reorder the terms:
90 + r = 102

Solving
90 + r = 102

Solving for variable 'r'.

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

Add '-90' to each side of the equation.
90 + -90 + r = 102 + -90

Combine like terms: 90 + -90 = 0
0 + r = 102 + -90
r = 102 + -90

Combine like terms: 102 + -90 = 12
r = 12

Simplifying
r = 12


Subproblem 2
r + 90 = -102

Simplifying
r + 90 = -102

Reorder the terms:
90 + r = -102

Solving
90 + r = -102

Solving for variable 'r'.

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

Add '-90' to each side of the equation.
90 + -90 + r = -102 + -90

Combine like terms: 90 + -90 = 0
0 + r = -102 + -90
r = -102 + -90

Combine like terms: -102 + -90 = -192
r = -192

Simplifying
r = -192


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {12, -192}

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