3668.8388=2*3.14r^2+2*3.14r*40.4

Simple and best practice solution for 3668.8388=2*3.14r^2+2*3.14r*40.4 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 3668.8388=2*3.14r^2+2*3.14r*40.4 equation: 


Simplifying
3668.8388 = 2 * 3.14r2 + 2 * 3.14r * 40.4

Multiply 2 * 3.14
3668.8388 = 6.28r2 + 2 * 3.14r * 40.4

Reorder the terms for easier multiplication:
3668.8388 = 6.28r2 + 2 * 3.14 * 40.4r

Multiply 2 * 3.14
3668.8388 = 6.28r2 + 6.28 * 40.4r

Multiply 6.28 * 40.4
3668.8388 = 6.28r2 + 253.712r

Reorder the terms:
3668.8388 = 253.712r + 6.28r2

Solving
3668.8388 = 253.712r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
3668.8388 + -253.712r + -6.28r2 = 253.712r + -253.712r + 6.28r2 + -6.28r2

Combine like terms: 253.712r + -253.712r = 0.000
3668.8388 + -253.712r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
3668.8388 + -253.712r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3668.8388 + -253.712r + -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'.
-584.21 + 40.4r + r2 = 0

Move the constant term to the right:

Add '584.21' to each side of the equation.
-584.21 + 40.4r + 584.21 + r2 = 0 + 584.21

Reorder the terms:
-584.21 + 584.21 + 40.4r + r2 = 0 + 584.21

Combine like terms: -584.21 + 584.21 = 0.00
0.00 + 40.4r + r2 = 0 + 584.21
40.4r + r2 = 0 + 584.21

Combine like terms: 0 + 584.21 = 584.21
40.4r + r2 = 584.21

The r term is 40.4r.  Take half its coefficient (20.2).
Square it (408.04) and add it to both sides.

Add '408.04' to each side of the equation.
40.4r + 408.04 + r2 = 584.21 + 408.04

Reorder the terms:
408.04 + 40.4r + r2 = 584.21 + 408.04

Combine like terms: 584.21 + 408.04 = 992.25
408.04 + 40.4r + r2 = 992.25

Factor a perfect square on the left side:
(r + 20.2)(r + 20.2) = 992.25

Calculate the square root of the right side: 31.5

Break this problem into two subproblems by setting 
(r + 20.2) equal to 31.5 and -31.5.


Subproblem 1
r + 20.2 = 31.5

Simplifying
r + 20.2 = 31.5

Reorder the terms:
20.2 + r = 31.5

Solving
20.2 + r = 31.5

Solving for variable 'r'.

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

Add '-20.2' to each side of the equation.
20.2 + -20.2 + r = 31.5 + -20.2

Combine like terms: 20.2 + -20.2 = 0.0
0.0 + r = 31.5 + -20.2
r = 31.5 + -20.2

Combine like terms: 31.5 + -20.2 = 11.3
r = 11.3

Simplifying
r = 11.3


Subproblem 2
r + 20.2 = -31.5

Simplifying
r + 20.2 = -31.5

Reorder the terms:
20.2 + r = -31.5

Solving
20.2 + r = -31.5

Solving for variable 'r'.

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

Add '-20.2' to each side of the equation.
20.2 + -20.2 + r = -31.5 + -20.2

Combine like terms: 20.2 + -20.2 = 0.0
0.0 + r = -31.5 + -20.2
r = -31.5 + -20.2

Combine like terms: -31.5 + -20.2 = -51.7
r = -51.7

Simplifying
r = -51.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {11.3, -51.7}

See similar equations:

| 10(-7+4n)=30 | | 21.57=4g+3.85 | | 6n+1=37 | | 0.4(0.95-0.05n)=0.33 | | z^2-26z+c=0 | | 5x-8=8x+13 | | 10+6h=-2b | | b-7+7b=32 | | 4x+2x+24=90 | | 3x+6x+18=90 | | 7x^3+21x=0 | | 5.1=6.3-0.4x | | Ln(4x-7)+ln(x-5)=2lnx | | 1.9=7.5-0.8x | | -24+12x-9x=15 | | 42.46=9g+3.67 | | -50-8x+3x=20 | | x+40=6 | | 4y=6x-16 | | 2x-8x-74=28 | | 56m=9m | | 2(2x+3)=3x-4 | | 12x-3x-81=144 | | 8/4=1/x | | -10(6x+6)=-360 | | A+14=-5a-2 | | 12t-21=-3t+9 | | 15x+45=0 | | =64x^3-27 | | 10(-5x+5)=-500 | | =64x^2-27 | | 3x+3-3=-6 |

Equations solver categories