314.1592654*r+3.141592654*r^2=3000

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Solution for 314.1592654*r+3.141592654*r^2=3000 equation:


Simplifying
314.1592654r + 3.141592654r2 = 3000

Solving
314.1592654r + 3.141592654r2 = 3000

Solving for variable 'r'.

Reorder the terms:
-3000 + 314.1592654r + 3.141592654r2 = 3000 + -3000

Combine like terms: 3000 + -3000 = 0
-3000 + 314.1592654r + 3.141592654r2 = 0

Begin completing the square.  Divide all terms by
3.141592654 the coefficient of the squared term: 

Divide each side by '3.141592654'.
-954.9296584 + 100r + r2 = 0

Move the constant term to the right:

Add '954.9296584' to each side of the equation.
-954.9296584 + 100r + 954.9296584 + r2 = 0 + 954.9296584

Reorder the terms:
-954.9296584 + 954.9296584 + 100r + r2 = 0 + 954.9296584

Combine like terms: -954.9296584 + 954.9296584 = 0.0000000
0.0000000 + 100r + r2 = 0 + 954.9296584
100r + r2 = 0 + 954.9296584

Combine like terms: 0 + 954.9296584 = 954.9296584
100r + r2 = 954.9296584

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 = 954.9296584 + 2500

Reorder the terms:
2500 + 100r + r2 = 954.9296584 + 2500

Combine like terms: 954.9296584 + 2500 = 3454.9296584
2500 + 100r + r2 = 3454.9296584

Factor a perfect square on the left side:
(r + 50)(r + 50) = 3454.9296584

Calculate the square root of the right side: 58.778649682

Break this problem into two subproblems by setting 
(r + 50) equal to 58.778649682 and -58.778649682.

Subproblem 1

r + 50 = 58.778649682 Simplifying r + 50 = 58.778649682 Reorder the terms: 50 + r = 58.778649682 Solving 50 + r = 58.778649682 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 = 58.778649682 + -50 Combine like terms: 50 + -50 = 0 0 + r = 58.778649682 + -50 r = 58.778649682 + -50 Combine like terms: 58.778649682 + -50 = 8.778649682 r = 8.778649682 Simplifying r = 8.778649682

Subproblem 2

r + 50 = -58.778649682 Simplifying r + 50 = -58.778649682 Reorder the terms: 50 + r = -58.778649682 Solving 50 + r = -58.778649682 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 = -58.778649682 + -50 Combine like terms: 50 + -50 = 0 0 + r = -58.778649682 + -50 r = -58.778649682 + -50 Combine like terms: -58.778649682 + -50 = -108.778649682 r = -108.778649682 Simplifying r = -108.778649682

Solution

The solution to the problem is based on the solutions from the subproblems. r = {8.778649682, -108.778649682}

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