8038.4=2*3.14*r^2+2*3.14*r*105

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Solution for 8038.4=2*3.14*r^2+2*3.14*r*105 equation: 


Simplifying
8038.4 = 2 * 3.14r2 + 2 * 3.14r * 105

Multiply 2 * 3.14
8038.4 = 6.28r2 + 2 * 3.14r * 105

Reorder the terms for easier multiplication:
8038.4 = 6.28r2 + 2 * 3.14 * 105r

Multiply 2 * 3.14
8038.4 = 6.28r2 + 6.28 * 105r

Multiply 6.28 * 105
8038.4 = 6.28r2 + 659.4r

Reorder the terms:
8038.4 = 659.4r + 6.28r2

Solving
8038.4 = 659.4r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
8038.4 + -659.4r + -6.28r2 = 659.4r + -659.4r + 6.28r2 + -6.28r2

Combine like terms: 659.4r + -659.4r = 0.0
8038.4 + -659.4r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
8038.4 + -659.4r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
8038.4 + -659.4r + -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'.
-1280 + 105r + r2 = 0

Move the constant term to the right:

Add '1280' to each side of the equation.
-1280 + 105r + 1280 + r2 = 0 + 1280

Reorder the terms:
-1280 + 1280 + 105r + r2 = 0 + 1280

Combine like terms: -1280 + 1280 = 0
0 + 105r + r2 = 0 + 1280
105r + r2 = 0 + 1280

Combine like terms: 0 + 1280 = 1280
105r + r2 = 1280

The r term is 105r.  Take half its coefficient (52.5).
Square it (2756.25) and add it to both sides.

Add '2756.25' to each side of the equation.
105r + 2756.25 + r2 = 1280 + 2756.25

Reorder the terms:
2756.25 + 105r + r2 = 1280 + 2756.25

Combine like terms: 1280 + 2756.25 = 4036.25
2756.25 + 105r + r2 = 4036.25

Factor a perfect square on the left side:
(r + 52.5)(r + 52.5) = 4036.25

Calculate the square root of the right side: 63.531488256

Break this problem into two subproblems by setting 
(r + 52.5) equal to 63.531488256 and -63.531488256.


Subproblem 1
r + 52.5 = 63.531488256

Simplifying
r + 52.5 = 63.531488256

Reorder the terms:
52.5 + r = 63.531488256

Solving
52.5 + r = 63.531488256

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-52.5' to each side of the equation.
52.5 + -52.5 + r = 63.531488256 + -52.5

Combine like terms: 52.5 + -52.5 = 0.0
0.0 + r = 63.531488256 + -52.5
r = 63.531488256 + -52.5

Combine like terms: 63.531488256 + -52.5 = 11.031488256
r = 11.031488256

Simplifying
r = 11.031488256


Subproblem 2
r + 52.5 = -63.531488256

Simplifying
r + 52.5 = -63.531488256

Reorder the terms:
52.5 + r = -63.531488256

Solving
52.5 + r = -63.531488256

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-52.5' to each side of the equation.
52.5 + -52.5 + r = -63.531488256 + -52.5

Combine like terms: 52.5 + -52.5 = 0.0
0.0 + r = -63.531488256 + -52.5
r = -63.531488256 + -52.5

Combine like terms: -63.531488256 + -52.5 = -116.031488256
r = -116.031488256

Simplifying
r = -116.031488256


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {11.031488256, -116.031488256}

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