2487.4452=6.28r^2+6.28r*40.8

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Solution for 2487.4452=6.28r^2+6.28r*40.8 equation: 


Simplifying
2487.4452 = 6.28r2 + 6.28r * 40.8

Reorder the terms for easier multiplication:
2487.4452 = 6.28r2 + 6.28 * 40.8r

Multiply 6.28 * 40.8
2487.4452 = 6.28r2 + 256.224r

Reorder the terms:
2487.4452 = 256.224r + 6.28r2

Solving
2487.4452 = 256.224r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
2487.4452 + -256.224r + -6.28r2 = 256.224r + -256.224r + 6.28r2 + -6.28r2

Combine like terms: 256.224r + -256.224r = 0.000
2487.4452 + -256.224r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
2487.4452 + -256.224r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
2487.4452 + -256.224r + -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'.
-396.09 + 40.8r + r2 = 0

Move the constant term to the right:

Add '396.09' to each side of the equation.
-396.09 + 40.8r + 396.09 + r2 = 0 + 396.09

Reorder the terms:
-396.09 + 396.09 + 40.8r + r2 = 0 + 396.09

Combine like terms: -396.09 + 396.09 = 0.00
0.00 + 40.8r + r2 = 0 + 396.09
40.8r + r2 = 0 + 396.09

Combine like terms: 0 + 396.09 = 396.09
40.8r + r2 = 396.09

The r term is 40.8r.  Take half its coefficient (20.4).
Square it (416.16) and add it to both sides.

Add '416.16' to each side of the equation.
40.8r + 416.16 + r2 = 396.09 + 416.16

Reorder the terms:
416.16 + 40.8r + r2 = 396.09 + 416.16

Combine like terms: 396.09 + 416.16 = 812.25
416.16 + 40.8r + r2 = 812.25

Factor a perfect square on the left side:
(r + 20.4)(r + 20.4) = 812.25

Calculate the square root of the right side: 28.5

Break this problem into two subproblems by setting 
(r + 20.4) equal to 28.5 and -28.5.


Subproblem 1
r + 20.4 = 28.5

Simplifying
r + 20.4 = 28.5

Reorder the terms:
20.4 + r = 28.5

Solving
20.4 + r = 28.5

Solving for variable 'r'.

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

Add '-20.4' to each side of the equation.
20.4 + -20.4 + r = 28.5 + -20.4

Combine like terms: 20.4 + -20.4 = 0.0
0.0 + r = 28.5 + -20.4
r = 28.5 + -20.4

Combine like terms: 28.5 + -20.4 = 8.1
r = 8.1

Simplifying
r = 8.1


Subproblem 2
r + 20.4 = -28.5

Simplifying
r + 20.4 = -28.5

Reorder the terms:
20.4 + r = -28.5

Solving
20.4 + r = -28.5

Solving for variable 'r'.

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

Add '-20.4' to each side of the equation.
20.4 + -20.4 + r = -28.5 + -20.4

Combine like terms: 20.4 + -20.4 = 0.0
0.0 + r = -28.5 + -20.4
r = -28.5 + -20.4

Combine like terms: -28.5 + -20.4 = -48.9
r = -48.9

Simplifying
r = -48.9


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {8.1, -48.9}

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