2*3.14*r^2+2*3.14*r*5=150.72

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Solution for 2*3.14*r^2+2*3.14*r*5=150.72 equation:


Simplifying
2 * 3.14r2 + 2 * 3.14r * 5 = 150.72

Multiply 2 * 3.14
6.28r2 + 2 * 3.14r * 5 = 150.72

Reorder the terms for easier multiplication:
6.28r2 + 2 * 3.14 * 5r = 150.72

Multiply 2 * 3.14
6.28r2 + 6.28 * 5r = 150.72

Multiply 6.28 * 5
6.28r2 + 31.4r = 150.72

Reorder the terms:
31.4r + 6.28r2 = 150.72

Solving
31.4r + 6.28r2 = 150.72

Solving for variable 'r'.

Reorder the terms:
-150.72 + 31.4r + 6.28r2 = 150.72 + -150.72

Combine like terms: 150.72 + -150.72 = 0.00
-150.72 + 31.4r + 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'.
-24 + 5r + r2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 5r + 24 + r2 = 0 + 24

Reorder the terms:
-24 + 24 + 5r + r2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 5r + r2 = 0 + 24
5r + r2 = 0 + 24

Combine like terms: 0 + 24 = 24
5r + r2 = 24

The r term is 5r.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5r + 6.25 + r2 = 24 + 6.25

Reorder the terms:
6.25 + 5r + r2 = 24 + 6.25

Combine like terms: 24 + 6.25 = 30.25
6.25 + 5r + r2 = 30.25

Factor a perfect square on the left side:
(r + 2.5)(r + 2.5) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(r + 2.5) equal to 5.5 and -5.5.

Subproblem 1

r + 2.5 = 5.5 Simplifying r + 2.5 = 5.5 Reorder the terms: 2.5 + r = 5.5 Solving 2.5 + r = 5.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = 5.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 5.5 + -2.5 r = 5.5 + -2.5 Combine like terms: 5.5 + -2.5 = 3 r = 3 Simplifying r = 3

Subproblem 2

r + 2.5 = -5.5 Simplifying r + 2.5 = -5.5 Reorder the terms: 2.5 + r = -5.5 Solving 2.5 + r = -5.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = -5.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -5.5 + -2.5 r = -5.5 + -2.5 Combine like terms: -5.5 + -2.5 = -8 r = -8 Simplifying r = -8

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3, -8}

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