14828.65=6.28r^2+6.28r

Simple and best practice solution for 14828.65=6.28r^2+6.28r 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 14828.65=6.28r^2+6.28r equation: 


Simplifying
14828.65 = 6.28r2 + 6.28r

Reorder the terms:
14828.65 = 6.28r + 6.28r2

Solving
14828.65 = 6.28r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
14828.65 + -6.28r + -6.28r2 = 6.28r + -6.28r + 6.28r2 + -6.28r2

Combine like terms: 6.28r + -6.28r = 0.00
14828.65 + -6.28r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
14828.65 + -6.28r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
14828.65 + -6.28r + -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'.
-2361.25 + r + r2 = 0

Move the constant term to the right:

Add '2361.25' to each side of the equation.
-2361.25 + r + 2361.25 + r2 = 0 + 2361.25

Reorder the terms:
-2361.25 + 2361.25 + r + r2 = 0 + 2361.25

Combine like terms: -2361.25 + 2361.25 = 0.00
0.00 + r + r2 = 0 + 2361.25
r + r2 = 0 + 2361.25

Combine like terms: 0 + 2361.25 = 2361.25
r + r2 = 2361.25

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + r2 = 2361.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + r2 = 2361.25 + 0.25

Combine like terms: 2361.25 + 0.25 = 2361.5
1.25 + r2 = 2361.5

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 2361.5

Calculate the square root of the right side: 48.595267259

Break this problem into two subproblems by setting 
(r + 0.5) equal to 48.595267259 and -48.595267259.


Subproblem 1
r + 0.5 = 48.595267259

Simplifying
r + 0.5 = 48.595267259

Reorder the terms:
0.5 + r = 48.595267259

Solving
0.5 + r = 48.595267259

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 48.595267259 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 48.595267259 + -0.5
r = 48.595267259 + -0.5

Combine like terms: 48.595267259 + -0.5 = 48.095267259
r = 48.095267259

Simplifying
r = 48.095267259


Subproblem 2
r + 0.5 = -48.595267259

Simplifying
r + 0.5 = -48.595267259

Reorder the terms:
0.5 + r = -48.595267259

Solving
0.5 + r = -48.595267259

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -48.595267259 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -48.595267259 + -0.5
r = -48.595267259 + -0.5

Combine like terms: -48.595267259 + -0.5 = -49.095267259
r = -49.095267259

Simplifying
r = -49.095267259


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {48.095267259, -49.095267259}

See similar equations:

| 3(x+2)-18=x-14 | | 9x^3=6 | | 3(x+2)-18=3x-12 | | 3(x-18)+2=3x-52 | | w/5-8=-28 | | 0=r^2-23.04 | | 2s+3t=22 | | 26=5+3v | | 2=2y-2 | | [4-(5-3(3-5)+2)]+4= | | 7p+8q=29 | | 65X-78Y=3 | | 3p+4q=13 | | u/5-14=27 | | 4x+1=3x-9 | | 3w+12=36 | | -v-10=-6v | | 7-4=-9 | | 27=x/4-11 | | 2y+11=35 | | 7x+6-3x=3x-5 | | 7(y-6)=21 | | -1/3(x-9)=4 | | 0=6.28r^2+1130.4r-14469.12 | | z/9=7 | | 3-5y=-17 | | 3=t/9 | | x^3+19x^2=0 | | 18-a/3=-5 | | (10x-25)/5 | | 0=r^2-112.36 | | x+32-2=20 |

Equations solver categories