7009.2336=6.28r^2+6.28r(64.4)

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Solution for 7009.2336=6.28r^2+6.28r(64.4) equation: 


Simplifying
7009.2336 = 6.28r2 + 6.28r(64.4)

Reorder the terms for easier multiplication:
7009.2336 = 6.28r2 + 6.28 * 64.4r

Multiply 6.28 * 64.4
7009.2336 = 6.28r2 + 404.432r

Reorder the terms:
7009.2336 = 404.432r + 6.28r2

Solving
7009.2336 = 404.432r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
7009.2336 + -404.432r + -6.28r2 = 404.432r + -404.432r + 6.28r2 + -6.28r2

Combine like terms: 404.432r + -404.432r = 0.000
7009.2336 + -404.432r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
7009.2336 + -404.432r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
7009.2336 + -404.432r + -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'.
-1116.12 + 64.4r + r2 = 0

Move the constant term to the right:

Add '1116.12' to each side of the equation.
-1116.12 + 64.4r + 1116.12 + r2 = 0 + 1116.12

Reorder the terms:
-1116.12 + 1116.12 + 64.4r + r2 = 0 + 1116.12

Combine like terms: -1116.12 + 1116.12 = 0.00
0.00 + 64.4r + r2 = 0 + 1116.12
64.4r + r2 = 0 + 1116.12

Combine like terms: 0 + 1116.12 = 1116.12
64.4r + r2 = 1116.12

The r term is 64.4r.  Take half its coefficient (32.2).
Square it (1036.84) and add it to both sides.

Add '1036.84' to each side of the equation.
64.4r + 1036.84 + r2 = 1116.12 + 1036.84

Reorder the terms:
1036.84 + 64.4r + r2 = 1116.12 + 1036.84

Combine like terms: 1116.12 + 1036.84 = 2152.96
1036.84 + 64.4r + r2 = 2152.96

Factor a perfect square on the left side:
(r + 32.2)(r + 32.2) = 2152.96

Calculate the square root of the right side: 46.4

Break this problem into two subproblems by setting 
(r + 32.2) equal to 46.4 and -46.4.


Subproblem 1
r + 32.2 = 46.4

Simplifying
r + 32.2 = 46.4

Reorder the terms:
32.2 + r = 46.4

Solving
32.2 + r = 46.4

Solving for variable 'r'.

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

Add '-32.2' to each side of the equation.
32.2 + -32.2 + r = 46.4 + -32.2

Combine like terms: 32.2 + -32.2 = 0.0
0.0 + r = 46.4 + -32.2
r = 46.4 + -32.2

Combine like terms: 46.4 + -32.2 = 14.2
r = 14.2

Simplifying
r = 14.2


Subproblem 2
r + 32.2 = -46.4

Simplifying
r + 32.2 = -46.4

Reorder the terms:
32.2 + r = -46.4

Solving
32.2 + r = -46.4

Solving for variable 'r'.

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

Add '-32.2' to each side of the equation.
32.2 + -32.2 + r = -46.4 + -32.2

Combine like terms: 32.2 + -32.2 = 0.0
0.0 + r = -46.4 + -32.2
r = -46.4 + -32.2

Combine like terms: -46.4 + -32.2 = -78.6
r = -78.6

Simplifying
r = -78.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {14.2, -78.6}

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