0=6.28r^2+66.568r-355.134

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Solution for 0=6.28r^2+66.568r-355.134 equation:


Simplifying
0 = 6.28r2 + 66.568r + -355.134

Reorder the terms:
0 = -355.134 + 66.568r + 6.28r2

Solving
0 = -355.134 + 66.568r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 355.134 = 355.134
355.134 + -66.568r + -6.28r2 = -355.134 + 66.568r + 6.28r2 + 355.134 + -66.568r + -6.28r2

Reorder the terms:
355.134 + -66.568r + -6.28r2 = -355.134 + 355.134 + 66.568r + -66.568r + 6.28r2 + -6.28r2

Combine like terms: -355.134 + 355.134 = 0.000
355.134 + -66.568r + -6.28r2 = 0.000 + 66.568r + -66.568r + 6.28r2 + -6.28r2
355.134 + -66.568r + -6.28r2 = 66.568r + -66.568r + 6.28r2 + -6.28r2

Combine like terms: 66.568r + -66.568r = 0.000
355.134 + -66.568r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
355.134 + -66.568r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
355.134 + -66.568r + -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'.
-56.55 + 10.6r + r2 = 0

Move the constant term to the right:

Add '56.55' to each side of the equation.
-56.55 + 10.6r + 56.55 + r2 = 0 + 56.55

Reorder the terms:
-56.55 + 56.55 + 10.6r + r2 = 0 + 56.55

Combine like terms: -56.55 + 56.55 = 0.00
0.00 + 10.6r + r2 = 0 + 56.55
10.6r + r2 = 0 + 56.55

Combine like terms: 0 + 56.55 = 56.55
10.6r + r2 = 56.55

The r term is 10.6r.  Take half its coefficient (5.3).
Square it (28.09) and add it to both sides.

Add '28.09' to each side of the equation.
10.6r + 28.09 + r2 = 56.55 + 28.09

Reorder the terms:
28.09 + 10.6r + r2 = 56.55 + 28.09

Combine like terms: 56.55 + 28.09 = 84.64
28.09 + 10.6r + r2 = 84.64

Factor a perfect square on the left side:
(r + 5.3)(r + 5.3) = 84.64

Calculate the square root of the right side: 9.2

Break this problem into two subproblems by setting 
(r + 5.3) equal to 9.2 and -9.2.

Subproblem 1

r + 5.3 = 9.2 Simplifying r + 5.3 = 9.2 Reorder the terms: 5.3 + r = 9.2 Solving 5.3 + r = 9.2 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + r = 9.2 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + r = 9.2 + -5.3 r = 9.2 + -5.3 Combine like terms: 9.2 + -5.3 = 3.9 r = 3.9 Simplifying r = 3.9

Subproblem 2

r + 5.3 = -9.2 Simplifying r + 5.3 = -9.2 Reorder the terms: 5.3 + r = -9.2 Solving 5.3 + r = -9.2 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + r = -9.2 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + r = -9.2 + -5.3 r = -9.2 + -5.3 Combine like terms: -9.2 + -5.3 = -14.5 r = -14.5 Simplifying r = -14.5

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.9, -14.5}

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