509.8104=2*3.14r^2+2*3.14*15.7r

Simple and best practice solution for 509.8104=2*3.14r^2+2*3.14*15.7r 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 509.8104=2*3.14r^2+2*3.14*15.7r equation: 


Simplifying
509.8104 = 2 * 3.14r2 + 2 * 3.14 * 15.7r

Multiply 2 * 3.14
509.8104 = 6.28r2 + 2 * 3.14 * 15.7r

Multiply 2 * 3.14
509.8104 = 6.28r2 + 6.28 * 15.7r

Multiply 6.28 * 15.7
509.8104 = 6.28r2 + 98.596r

Reorder the terms:
509.8104 = 98.596r + 6.28r2

Solving
509.8104 = 98.596r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
509.8104 + -98.596r + -6.28r2 = 98.596r + -98.596r + 6.28r2 + -6.28r2

Combine like terms: 98.596r + -98.596r = 0.000
509.8104 + -98.596r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
509.8104 + -98.596r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
509.8104 + -98.596r + -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'.
-81.18 + 15.7r + r2 = 0

Move the constant term to the right:

Add '81.18' to each side of the equation.
-81.18 + 15.7r + 81.18 + r2 = 0 + 81.18

Reorder the terms:
-81.18 + 81.18 + 15.7r + r2 = 0 + 81.18

Combine like terms: -81.18 + 81.18 = 0.00
0.00 + 15.7r + r2 = 0 + 81.18
15.7r + r2 = 0 + 81.18

Combine like terms: 0 + 81.18 = 81.18
15.7r + r2 = 81.18

The r term is 15.7r.  Take half its coefficient (7.85).
Square it (61.6225) and add it to both sides.

Add '61.6225' to each side of the equation.
15.7r + 61.6225 + r2 = 81.18 + 61.6225

Reorder the terms:
61.6225 + 15.7r + r2 = 81.18 + 61.6225

Combine like terms: 81.18 + 61.6225 = 142.8025
61.6225 + 15.7r + r2 = 142.8025

Factor a perfect square on the left side:
(r + 7.85)(r + 7.85) = 142.8025

Calculate the square root of the right side: 11.95

Break this problem into two subproblems by setting 
(r + 7.85) equal to 11.95 and -11.95.


Subproblem 1
r + 7.85 = 11.95

Simplifying
r + 7.85 = 11.95

Reorder the terms:
7.85 + r = 11.95

Solving
7.85 + r = 11.95

Solving for variable 'r'.

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

Add '-7.85' to each side of the equation.
7.85 + -7.85 + r = 11.95 + -7.85

Combine like terms: 7.85 + -7.85 = 0.00
0.00 + r = 11.95 + -7.85
r = 11.95 + -7.85

Combine like terms: 11.95 + -7.85 = 4.1
r = 4.1

Simplifying
r = 4.1


Subproblem 2
r + 7.85 = -11.95

Simplifying
r + 7.85 = -11.95

Reorder the terms:
7.85 + r = -11.95

Solving
7.85 + r = -11.95

Solving for variable 'r'.

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

Add '-7.85' to each side of the equation.
7.85 + -7.85 + r = -11.95 + -7.85

Combine like terms: 7.85 + -7.85 = 0.00
0.00 + r = -11.95 + -7.85
r = -11.95 + -7.85

Combine like terms: -11.95 + -7.85 = -19.8
r = -19.8

Simplifying
r = -19.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.1, -19.8}

See similar equations:

| xy-5x-3y+18=0 | | 3/5.12/x.y/75 | | 6.5+y=16 | | 3x^2+8y^2=1 | | -21-2a=6(-7-a)+1 | | y-1.5=9.7 | | Y^6-3=11 | | 3q^4x2q^5/q^3 | | 9(x+4)=2x-3 | | 4x-8y=18 | | 6.2=3t+4+2t | | 4/5(m-1)-1/5m | | 3sinhx-coshx=1 | | 4y+116=(7y+6) | | 117=-3-8(x-7) | | 33=3h | | (4x+5y)(4x+5y)= | | l=15-3u | | 8x+6y=-2k | | 17-x=1/3. | | -3.75=0.2+r | | 9x-2y=5k | | (1+m^2)x^2+(5m-10)x+17=0 | | -7(2y+6)=7(y-6) | | 6.2a=0.0124 | | 3x-5+3=4-5x | | 3(4s+8)=60 | | 16X^3-12X+3=0 | | 1.2y-0.5y=4.2 | | 1/6X=35 | | 5/8×A=2/5 | | 6m+10=4m-6 |

Equations solver categories