355.134=3.14*2*r^2+2*3.14*r*10.6

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Solution for 355.134=3.14*2*r^2+2*3.14*r*10.6 equation: 


Simplifying
355.134 = 3.14 * 2r2 + 2 * 3.14r * 10.6

Multiply 3.14 * 2
355.134 = 6.28r2 + 2 * 3.14r * 10.6

Reorder the terms for easier multiplication:
355.134 = 6.28r2 + 2 * 3.14 * 10.6r

Multiply 2 * 3.14
355.134 = 6.28r2 + 6.28 * 10.6r

Multiply 6.28 * 10.6
355.134 = 6.28r2 + 66.568r

Reorder the terms:
355.134 = 66.568r + 6.28r2

Solving
355.134 = 66.568r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
355.134 + -66.568r + -6.28r2 = 66.568r + -66.568r + 6.28r2 + -6.28r2

Combine like terms: 66.568r + -66.568r = 0.000
355.134 + -66.568r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
355.134 + -66.568r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
355.134 + -66.568r + -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'.
-56.55 + 10.6r + r2 = 0

Move the constant term to the right:

Add '56.55' to each side of the equation.
-56.55 + 10.6r + 56.55 + r2 = 0 + 56.55

Reorder the terms:
-56.55 + 56.55 + 10.6r + r2 = 0 + 56.55

Combine like terms: -56.55 + 56.55 = 0.00
0.00 + 10.6r + r2 = 0 + 56.55
10.6r + r2 = 0 + 56.55

Combine like terms: 0 + 56.55 = 56.55
10.6r + r2 = 56.55

The r term is 10.6r.  Take half its coefficient (5.3).
Square it (28.09) and add it to both sides.

Add '28.09' to each side of the equation.
10.6r + 28.09 + r2 = 56.55 + 28.09

Reorder the terms:
28.09 + 10.6r + r2 = 56.55 + 28.09

Combine like terms: 56.55 + 28.09 = 84.64
28.09 + 10.6r + r2 = 84.64

Factor a perfect square on the left side:
(r + 5.3)(r + 5.3) = 84.64

Calculate the square root of the right side: 9.2

Break this problem into two subproblems by setting 
(r + 5.3) equal to 9.2 and -9.2.


Subproblem 1
r + 5.3 = 9.2

Simplifying
r + 5.3 = 9.2

Reorder the terms:
5.3 + r = 9.2

Solving
5.3 + r = 9.2

Solving for variable 'r'.

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

Add '-5.3' to each side of the equation.
5.3 + -5.3 + r = 9.2 + -5.3

Combine like terms: 5.3 + -5.3 = 0.0
0.0 + r = 9.2 + -5.3
r = 9.2 + -5.3

Combine like terms: 9.2 + -5.3 = 3.9
r = 3.9

Simplifying
r = 3.9


Subproblem 2
r + 5.3 = -9.2

Simplifying
r + 5.3 = -9.2

Reorder the terms:
5.3 + r = -9.2

Solving
5.3 + r = -9.2

Solving for variable 'r'.

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

Add '-5.3' to each side of the equation.
5.3 + -5.3 + r = -9.2 + -5.3

Combine like terms: 5.3 + -5.3 = 0.0
0.0 + r = -9.2 + -5.3
r = -9.2 + -5.3

Combine like terms: -9.2 + -5.3 = -14.5
r = -14.5

Simplifying
r = -14.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.9, -14.5}

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