0=6.28r^2+401.92r-285.9912

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Solution for 0=6.28r^2+401.92r-285.9912 equation:


Simplifying
0 = 6.28r2 + 401.92r + -285.9912

Reorder the terms:
0 = -285.9912 + 401.92r + 6.28r2

Solving
0 = -285.9912 + 401.92r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 285.9912 = 285.9912
285.9912 + -401.92r + -6.28r2 = -285.9912 + 401.92r + 6.28r2 + 285.9912 + -401.92r + -6.28r2

Reorder the terms:
285.9912 + -401.92r + -6.28r2 = -285.9912 + 285.9912 + 401.92r + -401.92r + 6.28r2 + -6.28r2

Combine like terms: -285.9912 + 285.9912 = 0.0000
285.9912 + -401.92r + -6.28r2 = 0.0000 + 401.92r + -401.92r + 6.28r2 + -6.28r2
285.9912 + -401.92r + -6.28r2 = 401.92r + -401.92r + 6.28r2 + -6.28r2

Combine like terms: 401.92r + -401.92r = 0.00
285.9912 + -401.92r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
285.9912 + -401.92r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
285.9912 + -401.92r + -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'.
-45.54 + 64r + r2 = 0

Move the constant term to the right:

Add '45.54' to each side of the equation.
-45.54 + 64r + 45.54 + r2 = 0 + 45.54

Reorder the terms:
-45.54 + 45.54 + 64r + r2 = 0 + 45.54

Combine like terms: -45.54 + 45.54 = 0.00
0.00 + 64r + r2 = 0 + 45.54
64r + r2 = 0 + 45.54

Combine like terms: 0 + 45.54 = 45.54
64r + r2 = 45.54

The r term is 64r.  Take half its coefficient (32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
64r + 1024 + r2 = 45.54 + 1024

Reorder the terms:
1024 + 64r + r2 = 45.54 + 1024

Combine like terms: 45.54 + 1024 = 1069.54
1024 + 64r + r2 = 1069.54

Factor a perfect square on the left side:
(r + 32)(r + 32) = 1069.54

Calculate the square root of the right side: 32.703822407

Break this problem into two subproblems by setting 
(r + 32) equal to 32.703822407 and -32.703822407.

Subproblem 1

r + 32 = 32.703822407 Simplifying r + 32 = 32.703822407 Reorder the terms: 32 + r = 32.703822407 Solving 32 + r = 32.703822407 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + r = 32.703822407 + -32 Combine like terms: 32 + -32 = 0 0 + r = 32.703822407 + -32 r = 32.703822407 + -32 Combine like terms: 32.703822407 + -32 = 0.703822407 r = 0.703822407 Simplifying r = 0.703822407

Subproblem 2

r + 32 = -32.703822407 Simplifying r + 32 = -32.703822407 Reorder the terms: 32 + r = -32.703822407 Solving 32 + r = -32.703822407 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + r = -32.703822407 + -32 Combine like terms: 32 + -32 = 0 0 + r = -32.703822407 + -32 r = -32.703822407 + -32 Combine like terms: -32.703822407 + -32 = -64.703822407 r = -64.703822407 Simplifying r = -64.703822407

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.703822407, -64.703822407}

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