3000=3.14*100*r+3.14*r^2

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Solution for 3000=3.14*100*r+3.14*r^2 equation:


Simplifying
3000 = 3.14 * 100r + 3.14r2

Multiply 3.14 * 100
3000 = 314r + 3.14r2

Solving
3000 = 314r + 3.14r2

Solving for variable 'r'.

Reorder the terms:
3000 + -314r + -3.14r2 = 314r + -314r + 3.14r2 + -3.14r2

Combine like terms: 314r + -314r = 0
3000 + -314r + -3.14r2 = 0 + 3.14r2 + -3.14r2
3000 + -314r + -3.14r2 = 3.14r2 + -3.14r2

Combine like terms: 3.14r2 + -3.14r2 = 0.00
3000 + -314r + -3.14r2 = 0.00

Begin completing the square.  Divide all terms by
-3.14 the coefficient of the squared term: 

Divide each side by '-3.14'.
-955.4140127 + 100r + r2 = 0

Move the constant term to the right:

Add '955.4140127' to each side of the equation.
-955.4140127 + 100r + 955.4140127 + r2 = 0 + 955.4140127

Reorder the terms:
-955.4140127 + 955.4140127 + 100r + r2 = 0 + 955.4140127

Combine like terms: -955.4140127 + 955.4140127 = 0.0000000
0.0000000 + 100r + r2 = 0 + 955.4140127
100r + r2 = 0 + 955.4140127

Combine like terms: 0 + 955.4140127 = 955.4140127
100r + r2 = 955.4140127

The r term is 100r.  Take half its coefficient (50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
100r + 2500 + r2 = 955.4140127 + 2500

Reorder the terms:
2500 + 100r + r2 = 955.4140127 + 2500

Combine like terms: 955.4140127 + 2500 = 3455.4140127
2500 + 100r + r2 = 3455.4140127

Factor a perfect square on the left side:
(r + 50)(r + 50) = 3455.4140127

Calculate the square root of the right side: 58.782769692

Break this problem into two subproblems by setting 
(r + 50) equal to 58.782769692 and -58.782769692.

Subproblem 1

r + 50 = 58.782769692 Simplifying r + 50 = 58.782769692 Reorder the terms: 50 + r = 58.782769692 Solving 50 + r = 58.782769692 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + r = 58.782769692 + -50 Combine like terms: 50 + -50 = 0 0 + r = 58.782769692 + -50 r = 58.782769692 + -50 Combine like terms: 58.782769692 + -50 = 8.782769692 r = 8.782769692 Simplifying r = 8.782769692

Subproblem 2

r + 50 = -58.782769692 Simplifying r + 50 = -58.782769692 Reorder the terms: 50 + r = -58.782769692 Solving 50 + r = -58.782769692 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + r = -58.782769692 + -50 Combine like terms: 50 + -50 = 0 0 + r = -58.782769692 + -50 r = -58.782769692 + -50 Combine like terms: -58.782769692 + -50 = -108.782769692 r = -108.782769692 Simplifying r = -108.782769692

Solution

The solution to the problem is based on the solutions from the subproblems. r = {8.782769692, -108.782769692}

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