3523=2*3.14*r*40+2*3.14*r^2

Simple and best practice solution for 3523=2*3.14*r*40+2*3.14*r^2 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 3523=2*3.14*r*40+2*3.14*r^2 equation:


Simplifying
3523 = 2 * 3.14r * 40 + 2 * 3.14r2

Reorder the terms for easier multiplication:
3523 = 2 * 3.14 * 40r + 2 * 3.14r2

Multiply 2 * 3.14
3523 = 6.28 * 40r + 2 * 3.14r2

Multiply 6.28 * 40
3523 = 251.2r + 2 * 3.14r2

Multiply 2 * 3.14
3523 = 251.2r + 6.28r2

Solving
3523 = 251.2r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
3523 + -251.2r + -6.28r2 = 251.2r + -251.2r + 6.28r2 + -6.28r2

Combine like terms: 251.2r + -251.2r = 0.0
3523 + -251.2r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
3523 + -251.2r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3523 + -251.2r + -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'.
-560.9872611 + 40r + r2 = 0

Move the constant term to the right:

Add '560.9872611' to each side of the equation.
-560.9872611 + 40r + 560.9872611 + r2 = 0 + 560.9872611

Reorder the terms:
-560.9872611 + 560.9872611 + 40r + r2 = 0 + 560.9872611

Combine like terms: -560.9872611 + 560.9872611 = 0.0000000
0.0000000 + 40r + r2 = 0 + 560.9872611
40r + r2 = 0 + 560.9872611

Combine like terms: 0 + 560.9872611 = 560.9872611
40r + r2 = 560.9872611

The r term is 40r.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40r + 400 + r2 = 560.9872611 + 400

Reorder the terms:
400 + 40r + r2 = 560.9872611 + 400

Combine like terms: 560.9872611 + 400 = 960.9872611
400 + 40r + r2 = 960.9872611

Factor a perfect square on the left side:
(r + 20)(r + 20) = 960.9872611

Calculate the square root of the right side: 30.999794533

Break this problem into two subproblems by setting 
(r + 20) equal to 30.999794533 and -30.999794533.

Subproblem 1

r + 20 = 30.999794533 Simplifying r + 20 = 30.999794533 Reorder the terms: 20 + r = 30.999794533 Solving 20 + r = 30.999794533 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + r = 30.999794533 + -20 Combine like terms: 20 + -20 = 0 0 + r = 30.999794533 + -20 r = 30.999794533 + -20 Combine like terms: 30.999794533 + -20 = 10.999794533 r = 10.999794533 Simplifying r = 10.999794533

Subproblem 2

r + 20 = -30.999794533 Simplifying r + 20 = -30.999794533 Reorder the terms: 20 + r = -30.999794533 Solving 20 + r = -30.999794533 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + r = -30.999794533 + -20 Combine like terms: 20 + -20 = 0 0 + r = -30.999794533 + -20 r = -30.999794533 + -20 Combine like terms: -30.999794533 + -20 = -50.999794533 r = -50.999794533 Simplifying r = -50.999794533

Solution

The solution to the problem is based on the solutions from the subproblems. r = {10.999794533, -50.999794533}

See similar equations:

| 10x+3Y=48.6 | | 4x=9y+-19-4x-7y+13 | | 5(5+7)=x(11+x) | | x^4-8x^3-25x^2+44x+60=0 | | 4x^2+54xy-90y^2= | | (4x-3)=20 | | 5x+6-0.5x=3x-7 | | 13k=23.14 | | 15a-30p= | | 1/3*3.14*4*4*9 | | 12x^2+11xy-15y^2= | | 1/2(7x-y) | | 3.3=0.11*x | | -7(-3x+4)=224 | | 3.3(0.11)=x | | 7(9+3x)=-147 | | 0.2(45)=x | | 7(-4x-6)=182 | | 4(-3x-8)=-140 | | 17x+3=15x+8 | | 2(4+5x)=38 | | ac-2b=9c | | 3(1+2x)=21 | | 7(9+6x)=-441 | | 4x-2(-2y+5x)+6y= | | 5y+8n= | | 6(-8-5x)=-168 | | 1=b/3-7 | | 5(x+1)-7.5x=-2 | | 8=192 | | -3/14y=-15 | | 0=-16t^2+160t+3 |

Equations solver categories