509.8104=2*3.14r^2+2*15.7r

Simple and best practice solution for 509.8104=2*3.14r^2+2*15.7r 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 509.8104=2*3.14r^2+2*15.7r equation: 


Simplifying
509.8104 = 2 * 3.14r2 + 2 * 15.7r

Multiply 2 * 3.14
509.8104 = 6.28r2 + 2 * 15.7r

Multiply 2 * 15.7
509.8104 = 6.28r2 + 31.4r

Reorder the terms:
509.8104 = 31.4r + 6.28r2

Solving
509.8104 = 31.4r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
509.8104 + -31.4r + -6.28r2 = 31.4r + -31.4r + 6.28r2 + -6.28r2

Combine like terms: 31.4r + -31.4r = 0.0
509.8104 + -31.4r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
509.8104 + -31.4r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
509.8104 + -31.4r + -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'.
-81.18 + 5r + r2 = 0

Move the constant term to the right:

Add '81.18' to each side of the equation.
-81.18 + 5r + 81.18 + r2 = 0 + 81.18

Reorder the terms:
-81.18 + 81.18 + 5r + r2 = 0 + 81.18

Combine like terms: -81.18 + 81.18 = 0.00
0.00 + 5r + r2 = 0 + 81.18
5r + r2 = 0 + 81.18

Combine like terms: 0 + 81.18 = 81.18
5r + r2 = 81.18

The r term is 5r.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5r + 6.25 + r2 = 81.18 + 6.25

Reorder the terms:
6.25 + 5r + r2 = 81.18 + 6.25

Combine like terms: 81.18 + 6.25 = 87.43
6.25 + 5r + r2 = 87.43

Factor a perfect square on the left side:
(r + 2.5)(r + 2.5) = 87.43

Calculate the square root of the right side: 9.350401061

Break this problem into two subproblems by setting 
(r + 2.5) equal to 9.350401061 and -9.350401061.


Subproblem 1
r + 2.5 = 9.350401061

Simplifying
r + 2.5 = 9.350401061

Reorder the terms:
2.5 + r = 9.350401061

Solving
2.5 + r = 9.350401061

Solving for variable 'r'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = 9.350401061 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = 9.350401061 + -2.5
r = 9.350401061 + -2.5

Combine like terms: 9.350401061 + -2.5 = 6.850401061
r = 6.850401061

Simplifying
r = 6.850401061


Subproblem 2
r + 2.5 = -9.350401061

Simplifying
r + 2.5 = -9.350401061

Reorder the terms:
2.5 + r = -9.350401061

Solving
2.5 + r = -9.350401061

Solving for variable 'r'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = -9.350401061 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = -9.350401061 + -2.5
r = -9.350401061 + -2.5

Combine like terms: -9.350401061 + -2.5 = -11.850401061
r = -11.850401061

Simplifying
r = -11.850401061


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.850401061, -11.850401061}

See similar equations:

| (8y-7)-3y= | | 633.024=6.28r^2+101.736r | | 633024=6.28r^2+101.736r | | 0.15x=2y | | 2y=0.15x | | -4+h=3 | | 180=(3x+4)+(x-5)+(2x-5) | | 3/4x/9=27 | | 0.3x-7=8 | | 34-N+13=61 | | x-91=100 | | 0.25=44 | | 184=n+33 | | 9.x^2/3 | | 285.9912=6.28r^2+596.6r | | 9=1404/m | | (x-2)+(y-4)=36 | | a=60-30/15 | | Ln(5x+2)=0 | | x(-x+2.5)=0 | | 9.x^2/3^2 | | 22.77=r^2 | | 2+(3x+4)= | | 2a-36+5-a= | | 6*7-N+18=55 | | 6+(x+4)+6+(x+4)= | | 6+(x+4)+6+(x+4)=2+(3x+4)+2+(3x+4) | | 1x+3=3x+7 | | g(x)=2x-1/6 | | 0.1xy/0.05y | | y=tanx+3 | | 2x^2-20x+8=31-4x+x^2 |

Equations solver categories