965.3616=6.28r^2+6.28r*9.9

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Solution for 965.3616=6.28r^2+6.28r*9.9 equation: 


Simplifying
965.3616 = 6.28r2 + 6.28r * 9.9

Reorder the terms for easier multiplication:
965.3616 = 6.28r2 + 6.28 * 9.9r

Multiply 6.28 * 9.9
965.3616 = 6.28r2 + 62.172r

Reorder the terms:
965.3616 = 62.172r + 6.28r2

Solving
965.3616 = 62.172r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
965.3616 + -62.172r + -6.28r2 = 62.172r + -62.172r + 6.28r2 + -6.28r2

Combine like terms: 62.172r + -62.172r = 0.000
965.3616 + -62.172r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
965.3616 + -62.172r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
965.3616 + -62.172r + -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'.
-153.72 + 9.9r + r2 = 0

Move the constant term to the right:

Add '153.72' to each side of the equation.
-153.72 + 9.9r + 153.72 + r2 = 0 + 153.72

Reorder the terms:
-153.72 + 153.72 + 9.9r + r2 = 0 + 153.72

Combine like terms: -153.72 + 153.72 = 0.00
0.00 + 9.9r + r2 = 0 + 153.72
9.9r + r2 = 0 + 153.72

Combine like terms: 0 + 153.72 = 153.72
9.9r + r2 = 153.72

The r term is 9.9r.  Take half its coefficient (4.95).
Square it (24.5025) and add it to both sides.

Add '24.5025' to each side of the equation.
9.9r + 24.5025 + r2 = 153.72 + 24.5025

Reorder the terms:
24.5025 + 9.9r + r2 = 153.72 + 24.5025

Combine like terms: 153.72 + 24.5025 = 178.2225
24.5025 + 9.9r + r2 = 178.2225

Factor a perfect square on the left side:
(r + 4.95)(r + 4.95) = 178.2225

Calculate the square root of the right side: 13.35

Break this problem into two subproblems by setting 
(r + 4.95) equal to 13.35 and -13.35.


Subproblem 1
r + 4.95 = 13.35

Simplifying
r + 4.95 = 13.35

Reorder the terms:
4.95 + r = 13.35

Solving
4.95 + r = 13.35

Solving for variable 'r'.

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

Add '-4.95' to each side of the equation.
4.95 + -4.95 + r = 13.35 + -4.95

Combine like terms: 4.95 + -4.95 = 0.00
0.00 + r = 13.35 + -4.95
r = 13.35 + -4.95

Combine like terms: 13.35 + -4.95 = 8.4
r = 8.4

Simplifying
r = 8.4


Subproblem 2
r + 4.95 = -13.35

Simplifying
r + 4.95 = -13.35

Reorder the terms:
4.95 + r = -13.35

Solving
4.95 + r = -13.35

Solving for variable 'r'.

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

Add '-4.95' to each side of the equation.
4.95 + -4.95 + r = -13.35 + -4.95

Combine like terms: 4.95 + -4.95 = 0.00
0.00 + r = -13.35 + -4.95
r = -13.35 + -4.95

Combine like terms: -13.35 + -4.95 = -18.3
r = -18.3

Simplifying
r = -18.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {8.4, -18.3}

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