25722.88=2*3.14*r^2+2*3.14r*240

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Solution for 25722.88=2*3.14*r^2+2*3.14r*240 equation:


Simplifying
25722.88 = 2 * 3.14r2 + 2 * 3.14r * 240

Multiply 2 * 3.14
25722.88 = 6.28r2 + 2 * 3.14r * 240

Reorder the terms for easier multiplication:
25722.88 = 6.28r2 + 2 * 3.14 * 240r

Multiply 2 * 3.14
25722.88 = 6.28r2 + 6.28 * 240r

Multiply 6.28 * 240
25722.88 = 6.28r2 + 1507.2r

Reorder the terms:
25722.88 = 1507.2r + 6.28r2

Solving
25722.88 = 1507.2r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
25722.88 + -1507.2r + -6.28r2 = 1507.2r + -1507.2r + 6.28r2 + -6.28r2

Combine like terms: 1507.2r + -1507.2r = 0.0
25722.88 + -1507.2r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
25722.88 + -1507.2r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
25722.88 + -1507.2r + -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'.
-4096 + 240r + r2 = 0

Move the constant term to the right:

Add '4096' to each side of the equation.
-4096 + 240r + 4096 + r2 = 0 + 4096

Reorder the terms:
-4096 + 4096 + 240r + r2 = 0 + 4096

Combine like terms: -4096 + 4096 = 0
0 + 240r + r2 = 0 + 4096
240r + r2 = 0 + 4096

Combine like terms: 0 + 4096 = 4096
240r + r2 = 4096

The r term is 240r.  Take half its coefficient (120).
Square it (14400) and add it to both sides.

Add '14400' to each side of the equation.
240r + 14400 + r2 = 4096 + 14400

Reorder the terms:
14400 + 240r + r2 = 4096 + 14400

Combine like terms: 4096 + 14400 = 18496
14400 + 240r + r2 = 18496

Factor a perfect square on the left side:
(r + 120)(r + 120) = 18496

Calculate the square root of the right side: 136

Break this problem into two subproblems by setting 
(r + 120) equal to 136 and -136.

Subproblem 1

r + 120 = 136 Simplifying r + 120 = 136 Reorder the terms: 120 + r = 136 Solving 120 + r = 136 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + -120 + r = 136 + -120 Combine like terms: 120 + -120 = 0 0 + r = 136 + -120 r = 136 + -120 Combine like terms: 136 + -120 = 16 r = 16 Simplifying r = 16

Subproblem 2

r + 120 = -136 Simplifying r + 120 = -136 Reorder the terms: 120 + r = -136 Solving 120 + r = -136 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + -120 + r = -136 + -120 Combine like terms: 120 + -120 = 0 0 + r = -136 + -120 r = -136 + -120 Combine like terms: -136 + -120 = -256 r = -256 Simplifying r = -256

Solution

The solution to the problem is based on the solutions from the subproblems. r = {16, -256}

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