81650.99=6.28r^2+6.28r(287.8)

Simple and best practice solution for 81650.99=6.28r^2+6.28r(287.8) 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 81650.99=6.28r^2+6.28r(287.8) equation: 


Simplifying
81650.99 = 6.28r2 + 6.28r(287.8)

Reorder the terms for easier multiplication:
81650.99 = 6.28r2 + 6.28 * 287.8r

Multiply 6.28 * 287.8
81650.99 = 6.28r2 + 1807.384r

Reorder the terms:
81650.99 = 1807.384r + 6.28r2

Solving
81650.99 = 1807.384r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
81650.99 + -1807.384r + -6.28r2 = 1807.384r + -1807.384r + 6.28r2 + -6.28r2

Combine like terms: 1807.384r + -1807.384r = 0.000
81650.99 + -1807.384r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
81650.99 + -1807.384r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
81650.99 + -1807.384r + -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'.
-13001.75 + 287.8r + r2 = 0

Move the constant term to the right:

Add '13001.75' to each side of the equation.
-13001.75 + 287.8r + 13001.75 + r2 = 0 + 13001.75

Reorder the terms:
-13001.75 + 13001.75 + 287.8r + r2 = 0 + 13001.75

Combine like terms: -13001.75 + 13001.75 = 0.00
0.00 + 287.8r + r2 = 0 + 13001.75
287.8r + r2 = 0 + 13001.75

Combine like terms: 0 + 13001.75 = 13001.75
287.8r + r2 = 13001.75

The r term is 287.8r.  Take half its coefficient (143.9).
Square it (20707.21) and add it to both sides.

Add '20707.21' to each side of the equation.
287.8r + 20707.21 + r2 = 13001.75 + 20707.21

Reorder the terms:
20707.21 + 287.8r + r2 = 13001.75 + 20707.21

Combine like terms: 13001.75 + 20707.21 = 33708.96
20707.21 + 287.8r + r2 = 33708.96

Factor a perfect square on the left side:
(r + 143.9)(r + 143.9) = 33708.96

Calculate the square root of the right side: 183.6

Break this problem into two subproblems by setting 
(r + 143.9) equal to 183.6 and -183.6.


Subproblem 1
r + 143.9 = 183.6

Simplifying
r + 143.9 = 183.6

Reorder the terms:
143.9 + r = 183.6

Solving
143.9 + r = 183.6

Solving for variable 'r'.

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

Add '-143.9' to each side of the equation.
143.9 + -143.9 + r = 183.6 + -143.9

Combine like terms: 143.9 + -143.9 = 0.0
0.0 + r = 183.6 + -143.9
r = 183.6 + -143.9

Combine like terms: 183.6 + -143.9 = 39.7
r = 39.7

Simplifying
r = 39.7


Subproblem 2
r + 143.9 = -183.6

Simplifying
r + 143.9 = -183.6

Reorder the terms:
143.9 + r = -183.6

Solving
143.9 + r = -183.6

Solving for variable 'r'.

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

Add '-143.9' to each side of the equation.
143.9 + -143.9 + r = -183.6 + -143.9

Combine like terms: 143.9 + -143.9 = 0.0
0.0 + r = -183.6 + -143.9
r = -183.6 + -143.9

Combine like terms: -183.6 + -143.9 = -327.5
r = -327.5

Simplifying
r = -327.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {39.7, -327.5}

See similar equations:

| 2(8s-4)=33+5s | | -4v-35=-7(v+8) | | 2y+200=y+50 | | 11=-4+3X | | 5r^2+24r+5=0 | | -10=4v+6 | | 36=2y+2(y+6) | | -3b+8-5d=18 | | 22(3x-6)= | | 32=9(5b-7) | | 8m^2+10m+5=0 | | 3p-2=54 | | 9x-5x+2x=33-13+22 | | 8(1-3k)=-26 | | 2x-25=5x+17 | | 2(x+1)=3(x-3) | | 22=6v+7(v-8) | | 5(8h-6)=20 | | -6+6p=9(5p-18) | | 5x+8-7(x+1)=6x+4 | | 57=7+5x | | -14=5u+2(u+7) | | 4(X-3)=2x+13 | | 2+6r=11-3r | | -8=2-5v | | 22x^8y^2+11xy= | | -2+3(1-8f)=21 | | 621.72=6.28r^2+6.28r(18.1) | | 17+11b=-5(-4b+20) | | 16y= | | 14=-2(u+1) | | 3(2(0.3)-5)+31=14 |

Equations solver categories