2*3.14*r*105+2*3.14*r^2=16616.88

Simple and best practice solution for 2*3.14*r*105+2*3.14*r^2=16616.88 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 2*3.14*r*105+2*3.14*r^2=16616.88 equation:


Simplifying
2 * 3.14r * 105 + 2 * 3.14r2 = 16616.88

Reorder the terms for easier multiplication:
2 * 3.14 * 105r + 2 * 3.14r2 = 16616.88

Multiply 2 * 3.14
6.28 * 105r + 2 * 3.14r2 = 16616.88

Multiply 6.28 * 105
659.4r + 2 * 3.14r2 = 16616.88

Multiply 2 * 3.14
659.4r + 6.28r2 = 16616.88

Solving
659.4r + 6.28r2 = 16616.88

Solving for variable 'r'.

Reorder the terms:
-16616.88 + 659.4r + 6.28r2 = 16616.88 + -16616.88

Combine like terms: 16616.88 + -16616.88 = 0.00
-16616.88 + 659.4r + 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'.
-2646 + 105r + r2 = 0

Move the constant term to the right:

Add '2646' to each side of the equation.
-2646 + 105r + 2646 + r2 = 0 + 2646

Reorder the terms:
-2646 + 2646 + 105r + r2 = 0 + 2646

Combine like terms: -2646 + 2646 = 0
0 + 105r + r2 = 0 + 2646
105r + r2 = 0 + 2646

Combine like terms: 0 + 2646 = 2646
105r + r2 = 2646

The r term is 105r.  Take half its coefficient (52.5).
Square it (2756.25) and add it to both sides.

Add '2756.25' to each side of the equation.
105r + 2756.25 + r2 = 2646 + 2756.25

Reorder the terms:
2756.25 + 105r + r2 = 2646 + 2756.25

Combine like terms: 2646 + 2756.25 = 5402.25
2756.25 + 105r + r2 = 5402.25

Factor a perfect square on the left side:
(r + 52.5)(r + 52.5) = 5402.25

Calculate the square root of the right side: 73.5

Break this problem into two subproblems by setting 
(r + 52.5) equal to 73.5 and -73.5.

Subproblem 1

r + 52.5 = 73.5 Simplifying r + 52.5 = 73.5 Reorder the terms: 52.5 + r = 73.5 Solving 52.5 + r = 73.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + r = 73.5 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + r = 73.5 + -52.5 r = 73.5 + -52.5 Combine like terms: 73.5 + -52.5 = 21 r = 21 Simplifying r = 21

Subproblem 2

r + 52.5 = -73.5 Simplifying r + 52.5 = -73.5 Reorder the terms: 52.5 + r = -73.5 Solving 52.5 + r = -73.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + r = -73.5 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + r = -73.5 + -52.5 r = -73.5 + -52.5 Combine like terms: -73.5 + -52.5 = -126 r = -126 Simplifying r = -126

Solution

The solution to the problem is based on the solutions from the subproblems. r = {21, -126}

See similar equations:

| a=3.9-[-8] | | Kx^2+(K-3)x+3=-71 | | n*n=6.25 | | 1-n=n-1 | | n=3n-.5 | | .6n=1 | | n*n=.25 | | .09n=11 | | 3x^2+8x=32 | | -.125n=80 | | -5n-5n-5=5 | | 10n-9n+8n-7n+6n=10-9+8-7+6 | | n*n+9=34 | | 90-2c=60 | | 7x+13=6x+11 | | 3x-1=2-3x | | 0.8x-1=-x+8 | | 0.8x-1=-x-8 | | x+(x-0.1)*0.583=0.2 | | 2n+10=3n+5 | | 0.8x-5=-x-8 | | 0.8x-10=-x+8 | | n*n=64 | | x+(x-0.1)*5=0.20 | | .1n=100 | | -0.5x-5=3x+1 | | n-n=10-n | | 1.50(4x+5)=1.17 | | .5n+1.5n=-10 | | 5n-5=85 | | 10n=.5 | | x+(x*.079)=675 |

Equations solver categories