47533.32=2*3.14*r^2+2*3.14*r*243

Simple and best practice solution for 47533.32=2*3.14*r^2+2*3.14*r*243 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 47533.32=2*3.14*r^2+2*3.14*r*243 equation:


Simplifying
47533.32 = 2 * 3.14r2 + 2 * 3.14r * 243

Multiply 2 * 3.14
47533.32 = 6.28r2 + 2 * 3.14r * 243

Reorder the terms for easier multiplication:
47533.32 = 6.28r2 + 2 * 3.14 * 243r

Multiply 2 * 3.14
47533.32 = 6.28r2 + 6.28 * 243r

Multiply 6.28 * 243
47533.32 = 6.28r2 + 1526.04r

Reorder the terms:
47533.32 = 1526.04r + 6.28r2

Solving
47533.32 = 1526.04r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
47533.32 + -1526.04r + -6.28r2 = 1526.04r + -1526.04r + 6.28r2 + -6.28r2

Combine like terms: 1526.04r + -1526.04r = 0.00
47533.32 + -1526.04r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
47533.32 + -1526.04r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
47533.32 + -1526.04r + -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'.
-7569 + 243r + r2 = 0

Move the constant term to the right:

Add '7569' to each side of the equation.
-7569 + 243r + 7569 + r2 = 0 + 7569

Reorder the terms:
-7569 + 7569 + 243r + r2 = 0 + 7569

Combine like terms: -7569 + 7569 = 0
0 + 243r + r2 = 0 + 7569
243r + r2 = 0 + 7569

Combine like terms: 0 + 7569 = 7569
243r + r2 = 7569

The r term is 243r.  Take half its coefficient (121.5).
Square it (14762.25) and add it to both sides.

Add '14762.25' to each side of the equation.
243r + 14762.25 + r2 = 7569 + 14762.25

Reorder the terms:
14762.25 + 243r + r2 = 7569 + 14762.25

Combine like terms: 7569 + 14762.25 = 22331.25
14762.25 + 243r + r2 = 22331.25

Factor a perfect square on the left side:
(r + 121.5)(r + 121.5) = 22331.25

Calculate the square root of the right side: 149.436441339

Break this problem into two subproblems by setting 
(r + 121.5) equal to 149.436441339 and -149.436441339.

Subproblem 1

r + 121.5 = 149.436441339 Simplifying r + 121.5 = 149.436441339 Reorder the terms: 121.5 + r = 149.436441339 Solving 121.5 + r = 149.436441339 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-121.5' to each side of the equation. 121.5 + -121.5 + r = 149.436441339 + -121.5 Combine like terms: 121.5 + -121.5 = 0.0 0.0 + r = 149.436441339 + -121.5 r = 149.436441339 + -121.5 Combine like terms: 149.436441339 + -121.5 = 27.936441339 r = 27.936441339 Simplifying r = 27.936441339

Subproblem 2

r + 121.5 = -149.436441339 Simplifying r + 121.5 = -149.436441339 Reorder the terms: 121.5 + r = -149.436441339 Solving 121.5 + r = -149.436441339 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-121.5' to each side of the equation. 121.5 + -121.5 + r = -149.436441339 + -121.5 Combine like terms: 121.5 + -121.5 = 0.0 0.0 + r = -149.436441339 + -121.5 r = -149.436441339 + -121.5 Combine like terms: -149.436441339 + -121.5 = -270.936441339 r = -270.936441339 Simplifying r = -270.936441339

Solution

The solution to the problem is based on the solutions from the subproblems. r = {27.936441339, -270.936441339}

See similar equations:

| (4*4-7*7*V*V)+7*V*V=16 | | X=196/cos(65) | | 2x^2+3x-3=18 | | f(x)=ln(3-x) | | 4x(x)=-32x | | 5+7=2+16 | | V*V(V-1)=0 | | x-3/517/6 | | R=v^2-6v | | 2(4k-3)-13k+6+4= | | 5+7=11+7x | | 5x(x)-9=46 | | 2(2k+5)-10k+5+2= | | f(7)=4x-7 | | 1/5x5/5 | | 7x(x)+14=0 | | 2(4c-1)-1=4c+5 | | (2x)(lnX)=0 | | 2y+4y=-16-8 | | 51x=0.13 | | 6+9(7a)=4+8(6a) | | 5(x+6)=6x-3 | | 8(9x-8)+1=72x | | 4w^2-9=9w | | 2(7x-5)=14x-8 | | 3+3(2r-6)-3(4r+5)-8= | | 3x+15=202x | | 6x-1+=4x+9 | | t^3+31.06t^2+189.62t+989.40=0 | | 6x-4x=-1+9 | | 1.1111=(x2-70)/11.3 | | 2x-17=9+x |

Equations solver categories