2708.8152=2*3.14*r^2+2*3.14*r*38.3

Simple and best practice solution for 2708.8152=2*3.14*r^2+2*3.14*r*38.3 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 2708.8152=2*3.14*r^2+2*3.14*r*38.3 equation: 


Simplifying
2708.8152 = 2 * 3.14r2 + 2 * 3.14r * 38.3

Multiply 2 * 3.14
2708.8152 = 6.28r2 + 2 * 3.14r * 38.3

Reorder the terms for easier multiplication:
2708.8152 = 6.28r2 + 2 * 3.14 * 38.3r

Multiply 2 * 3.14
2708.8152 = 6.28r2 + 6.28 * 38.3r

Multiply 6.28 * 38.3
2708.8152 = 6.28r2 + 240.524r

Reorder the terms:
2708.8152 = 240.524r + 6.28r2

Solving
2708.8152 = 240.524r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
2708.8152 + -240.524r + -6.28r2 = 240.524r + -240.524r + 6.28r2 + -6.28r2

Combine like terms: 240.524r + -240.524r = 0.000
2708.8152 + -240.524r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
2708.8152 + -240.524r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
2708.8152 + -240.524r + -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'.
-431.34 + 38.3r + r2 = 0

Move the constant term to the right:

Add '431.34' to each side of the equation.
-431.34 + 38.3r + 431.34 + r2 = 0 + 431.34

Reorder the terms:
-431.34 + 431.34 + 38.3r + r2 = 0 + 431.34

Combine like terms: -431.34 + 431.34 = 0.00
0.00 + 38.3r + r2 = 0 + 431.34
38.3r + r2 = 0 + 431.34

Combine like terms: 0 + 431.34 = 431.34
38.3r + r2 = 431.34

The r term is 38.3r.  Take half its coefficient (19.15).
Square it (366.7225) and add it to both sides.

Add '366.7225' to each side of the equation.
38.3r + 366.7225 + r2 = 431.34 + 366.7225

Reorder the terms:
366.7225 + 38.3r + r2 = 431.34 + 366.7225

Combine like terms: 431.34 + 366.7225 = 798.0625
366.7225 + 38.3r + r2 = 798.0625

Factor a perfect square on the left side:
(r + 19.15)(r + 19.15) = 798.0625

Calculate the square root of the right side: 28.25

Break this problem into two subproblems by setting 
(r + 19.15) equal to 28.25 and -28.25.


Subproblem 1
r + 19.15 = 28.25

Simplifying
r + 19.15 = 28.25

Reorder the terms:
19.15 + r = 28.25

Solving
19.15 + r = 28.25

Solving for variable 'r'.

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

Add '-19.15' to each side of the equation.
19.15 + -19.15 + r = 28.25 + -19.15

Combine like terms: 19.15 + -19.15 = 0.00
0.00 + r = 28.25 + -19.15
r = 28.25 + -19.15

Combine like terms: 28.25 + -19.15 = 9.1
r = 9.1

Simplifying
r = 9.1


Subproblem 2
r + 19.15 = -28.25

Simplifying
r + 19.15 = -28.25

Reorder the terms:
19.15 + r = -28.25

Solving
19.15 + r = -28.25

Solving for variable 'r'.

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

Add '-19.15' to each side of the equation.
19.15 + -19.15 + r = -28.25 + -19.15

Combine like terms: 19.15 + -19.15 = 0.00
0.00 + r = -28.25 + -19.15
r = -28.25 + -19.15

Combine like terms: -28.25 + -19.15 = -47.4
r = -47.4

Simplifying
r = -47.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.1, -47.4}

See similar equations:

| 5x+2=3.5 | | 15x-3x-3=3+7 | | 2x-1.3=5.5 | | 3x=3.6 | | 4x+7y=514 | | x+1.2=7.5 | | 9-(2n-7)=2-3n | | 14x^2+48x+18=0 | | 10+5x=(23+3x) | | lny=lnx+ln(x+7)+lnC | | a+19+7a=6a+49 | | 2x+3x=10x | | e^7x+6=14 | | 8+5p=4p-1 | | 7(x+5)=6(x-7) | | 7+2k=k+1 | | 18=-4y | | 2t(t-1)=144 | | x^2+y^2+6x-8y+34=0 | | 0.33(6x+9)=3x | | 10(t)=-2t^2+20t+10 | | z^2-z+6=0 | | h(t)=-2t^2+20t+10 | | -4z-20=-2z+6 | | v-6-8v=-13 | | 5+2y-20y= | | 1.5xX=X | | 9x-10=10x+5 | | -2b+4b=6 | | 12s^2-12s+3=0 | | 1792=3.5x+8 | | U=3(8n+32)+5(n+1) |

Equations solver categories