1175.0508=6.28*r^2+6.28*r*23.4

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Solution for 1175.0508=6.28*r^2+6.28*r*23.4 equation: 


Simplifying
1175.0508 = 6.28r2 + 6.28r * 23.4

Reorder the terms for easier multiplication:
1175.0508 = 6.28r2 + 6.28 * 23.4r

Multiply 6.28 * 23.4
1175.0508 = 6.28r2 + 146.952r

Reorder the terms:
1175.0508 = 146.952r + 6.28r2

Solving
1175.0508 = 146.952r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
1175.0508 + -146.952r + -6.28r2 = 146.952r + -146.952r + 6.28r2 + -6.28r2

Combine like terms: 146.952r + -146.952r = 0.000
1175.0508 + -146.952r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
1175.0508 + -146.952r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
1175.0508 + -146.952r + -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'.
-187.11 + 23.4r + r2 = 0

Move the constant term to the right:

Add '187.11' to each side of the equation.
-187.11 + 23.4r + 187.11 + r2 = 0 + 187.11

Reorder the terms:
-187.11 + 187.11 + 23.4r + r2 = 0 + 187.11

Combine like terms: -187.11 + 187.11 = 0.00
0.00 + 23.4r + r2 = 0 + 187.11
23.4r + r2 = 0 + 187.11

Combine like terms: 0 + 187.11 = 187.11
23.4r + r2 = 187.11

The r term is 23.4r.  Take half its coefficient (11.7).
Square it (136.89) and add it to both sides.

Add '136.89' to each side of the equation.
23.4r + 136.89 + r2 = 187.11 + 136.89

Reorder the terms:
136.89 + 23.4r + r2 = 187.11 + 136.89

Combine like terms: 187.11 + 136.89 = 324
136.89 + 23.4r + r2 = 324

Factor a perfect square on the left side:
(r + 11.7)(r + 11.7) = 324

Calculate the square root of the right side: 18

Break this problem into two subproblems by setting 
(r + 11.7) equal to 18 and -18.


Subproblem 1
r + 11.7 = 18

Simplifying
r + 11.7 = 18

Reorder the terms:
11.7 + r = 18

Solving
11.7 + r = 18

Solving for variable 'r'.

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

Add '-11.7' to each side of the equation.
11.7 + -11.7 + r = 18 + -11.7

Combine like terms: 11.7 + -11.7 = 0.0
0.0 + r = 18 + -11.7
r = 18 + -11.7

Combine like terms: 18 + -11.7 = 6.3
r = 6.3

Simplifying
r = 6.3


Subproblem 2
r + 11.7 = -18

Simplifying
r + 11.7 = -18

Reorder the terms:
11.7 + r = -18

Solving
11.7 + r = -18

Solving for variable 'r'.

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

Add '-11.7' to each side of the equation.
11.7 + -11.7 + r = -18 + -11.7

Combine like terms: 11.7 + -11.7 = 0.0
0.0 + r = -18 + -11.7
r = -18 + -11.7

Combine like terms: -18 + -11.7 = -29.7
r = -29.7

Simplifying
r = -29.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.3, -29.7}

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