159.3864=2*3.14*r^2+2*3.14*r*6.7

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Solution for 159.3864=2*3.14*r^2+2*3.14*r*6.7 equation: 


Simplifying
159.3864 = 2 * 3.14r2 + 2 * 3.14r * 6.7

Multiply 2 * 3.14
159.3864 = 6.28r2 + 2 * 3.14r * 6.7

Reorder the terms for easier multiplication:
159.3864 = 6.28r2 + 2 * 3.14 * 6.7r

Multiply 2 * 3.14
159.3864 = 6.28r2 + 6.28 * 6.7r

Multiply 6.28 * 6.7
159.3864 = 6.28r2 + 42.076r

Reorder the terms:
159.3864 = 42.076r + 6.28r2

Solving
159.3864 = 42.076r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
159.3864 + -42.076r + -6.28r2 = 42.076r + -42.076r + 6.28r2 + -6.28r2

Combine like terms: 42.076r + -42.076r = 0.000
159.3864 + -42.076r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
159.3864 + -42.076r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
159.3864 + -42.076r + -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'.
-25.38 + 6.7r + r2 = 0

Move the constant term to the right:

Add '25.38' to each side of the equation.
-25.38 + 6.7r + 25.38 + r2 = 0 + 25.38

Reorder the terms:
-25.38 + 25.38 + 6.7r + r2 = 0 + 25.38

Combine like terms: -25.38 + 25.38 = 0.00
0.00 + 6.7r + r2 = 0 + 25.38
6.7r + r2 = 0 + 25.38

Combine like terms: 0 + 25.38 = 25.38
6.7r + r2 = 25.38

The r term is 6.7r.  Take half its coefficient (3.35).
Square it (11.2225) and add it to both sides.

Add '11.2225' to each side of the equation.
6.7r + 11.2225 + r2 = 25.38 + 11.2225

Reorder the terms:
11.2225 + 6.7r + r2 = 25.38 + 11.2225

Combine like terms: 25.38 + 11.2225 = 36.6025
11.2225 + 6.7r + r2 = 36.6025

Factor a perfect square on the left side:
(r + 3.35)(r + 3.35) = 36.6025

Calculate the square root of the right side: 6.05

Break this problem into two subproblems by setting 
(r + 3.35) equal to 6.05 and -6.05.


Subproblem 1
r + 3.35 = 6.05

Simplifying
r + 3.35 = 6.05

Reorder the terms:
3.35 + r = 6.05

Solving
3.35 + r = 6.05

Solving for variable 'r'.

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

Add '-3.35' to each side of the equation.
3.35 + -3.35 + r = 6.05 + -3.35

Combine like terms: 3.35 + -3.35 = 0.00
0.00 + r = 6.05 + -3.35
r = 6.05 + -3.35

Combine like terms: 6.05 + -3.35 = 2.7
r = 2.7

Simplifying
r = 2.7


Subproblem 2
r + 3.35 = -6.05

Simplifying
r + 3.35 = -6.05

Reorder the terms:
3.35 + r = -6.05

Solving
3.35 + r = -6.05

Solving for variable 'r'.

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

Add '-3.35' to each side of the equation.
3.35 + -3.35 + r = -6.05 + -3.35

Combine like terms: 3.35 + -3.35 = 0.00
0.00 + r = -6.05 + -3.35
r = -6.05 + -3.35

Combine like terms: -6.05 + -3.35 = -9.4
r = -9.4

Simplifying
r = -9.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.7, -9.4}

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