24115.2=6.28*r^2+6.28*r*195

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Solution for 24115.2=6.28*r^2+6.28*r*195 equation:


Simplifying
24115.2 = 6.28r2 + 6.28r * 195

Reorder the terms for easier multiplication:
24115.2 = 6.28r2 + 6.28 * 195r

Multiply 6.28 * 195
24115.2 = 6.28r2 + 1224.6r

Reorder the terms:
24115.2 = 1224.6r + 6.28r2

Solving
24115.2 = 1224.6r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
24115.2 + -1224.6r + -6.28r2 = 1224.6r + -1224.6r + 6.28r2 + -6.28r2

Combine like terms: 1224.6r + -1224.6r = 0.0
24115.2 + -1224.6r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
24115.2 + -1224.6r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
24115.2 + -1224.6r + -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'.
-3840 + 195r + r2 = 0

Move the constant term to the right:

Add '3840' to each side of the equation.
-3840 + 195r + 3840 + r2 = 0 + 3840

Reorder the terms:
-3840 + 3840 + 195r + r2 = 0 + 3840

Combine like terms: -3840 + 3840 = 0
0 + 195r + r2 = 0 + 3840
195r + r2 = 0 + 3840

Combine like terms: 0 + 3840 = 3840
195r + r2 = 3840

The r term is 195r.  Take half its coefficient (97.5).
Square it (9506.25) and add it to both sides.

Add '9506.25' to each side of the equation.
195r + 9506.25 + r2 = 3840 + 9506.25

Reorder the terms:
9506.25 + 195r + r2 = 3840 + 9506.25

Combine like terms: 3840 + 9506.25 = 13346.25
9506.25 + 195r + r2 = 13346.25

Factor a perfect square on the left side:
(r + 97.5)(r + 97.5) = 13346.25

Calculate the square root of the right side: 115.525971106

Break this problem into two subproblems by setting 
(r + 97.5) equal to 115.525971106 and -115.525971106.

Subproblem 1

r + 97.5 = 115.525971106 Simplifying r + 97.5 = 115.525971106 Reorder the terms: 97.5 + r = 115.525971106 Solving 97.5 + r = 115.525971106 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-97.5' to each side of the equation. 97.5 + -97.5 + r = 115.525971106 + -97.5 Combine like terms: 97.5 + -97.5 = 0.0 0.0 + r = 115.525971106 + -97.5 r = 115.525971106 + -97.5 Combine like terms: 115.525971106 + -97.5 = 18.025971106 r = 18.025971106 Simplifying r = 18.025971106

Subproblem 2

r + 97.5 = -115.525971106 Simplifying r + 97.5 = -115.525971106 Reorder the terms: 97.5 + r = -115.525971106 Solving 97.5 + r = -115.525971106 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-97.5' to each side of the equation. 97.5 + -97.5 + r = -115.525971106 + -97.5 Combine like terms: 97.5 + -97.5 = 0.0 0.0 + r = -115.525971106 + -97.5 r = -115.525971106 + -97.5 Combine like terms: -115.525971106 + -97.5 = -213.025971106 r = -213.025971106 Simplifying r = -213.025971106

Solution

The solution to the problem is based on the solutions from the subproblems. r = {18.025971106, -213.025971106}

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