285.9912=6.28r^2+596.6r

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Solution for 285.9912=6.28r^2+596.6r equation:


Simplifying
285.9912 = 6.28r2 + 596.6r

Reorder the terms:
285.9912 = 596.6r + 6.28r2

Solving
285.9912 = 596.6r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
285.9912 + -596.6r + -6.28r2 = 596.6r + -596.6r + 6.28r2 + -6.28r2

Combine like terms: 596.6r + -596.6r = 0.0
285.9912 + -596.6r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
285.9912 + -596.6r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
285.9912 + -596.6r + -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'.
-45.54 + 95r + r2 = 0

Move the constant term to the right:

Add '45.54' to each side of the equation.
-45.54 + 95r + 45.54 + r2 = 0 + 45.54

Reorder the terms:
-45.54 + 45.54 + 95r + r2 = 0 + 45.54

Combine like terms: -45.54 + 45.54 = 0.00
0.00 + 95r + r2 = 0 + 45.54
95r + r2 = 0 + 45.54

Combine like terms: 0 + 45.54 = 45.54
95r + r2 = 45.54

The r term is 95r.  Take half its coefficient (47.5).
Square it (2256.25) and add it to both sides.

Add '2256.25' to each side of the equation.
95r + 2256.25 + r2 = 45.54 + 2256.25

Reorder the terms:
2256.25 + 95r + r2 = 45.54 + 2256.25

Combine like terms: 45.54 + 2256.25 = 2301.79
2256.25 + 95r + r2 = 2301.79

Factor a perfect square on the left side:
(r + 47.5)(r + 47.5) = 2301.79

Calculate the square root of the right side: 47.976973644

Break this problem into two subproblems by setting 
(r + 47.5) equal to 47.976973644 and -47.976973644.

Subproblem 1

r + 47.5 = 47.976973644 Simplifying r + 47.5 = 47.976973644 Reorder the terms: 47.5 + r = 47.976973644 Solving 47.5 + r = 47.976973644 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + r = 47.976973644 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + r = 47.976973644 + -47.5 r = 47.976973644 + -47.5 Combine like terms: 47.976973644 + -47.5 = 0.476973644 r = 0.476973644 Simplifying r = 0.476973644

Subproblem 2

r + 47.5 = -47.976973644 Simplifying r + 47.5 = -47.976973644 Reorder the terms: 47.5 + r = -47.976973644 Solving 47.5 + r = -47.976973644 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + r = -47.976973644 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + r = -47.976973644 + -47.5 r = -47.976973644 + -47.5 Combine like terms: -47.976973644 + -47.5 = -95.476973644 r = -95.476973644 Simplifying r = -95.476973644

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.476973644, -95.476973644}

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