453.662=2*3.14*r^2+2*3.14*r*13

Simple and best practice solution for 453.662=2*3.14*r^2+2*3.14*r*13 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 453.662=2*3.14*r^2+2*3.14*r*13 equation:


Simplifying
453.662 = 2 * 3.14r2 + 2 * 3.14r * 13

Multiply 2 * 3.14
453.662 = 6.28r2 + 2 * 3.14r * 13

Reorder the terms for easier multiplication:
453.662 = 6.28r2 + 2 * 3.14 * 13r

Multiply 2 * 3.14
453.662 = 6.28r2 + 6.28 * 13r

Multiply 6.28 * 13
453.662 = 6.28r2 + 81.64r

Reorder the terms:
453.662 = 81.64r + 6.28r2

Solving
453.662 = 81.64r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
453.662 + -81.64r + -6.28r2 = 81.64r + -81.64r + 6.28r2 + -6.28r2

Combine like terms: 81.64r + -81.64r = 0.00
453.662 + -81.64r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
453.662 + -81.64r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
453.662 + -81.64r + -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'.
-72.23917197 + 13r + r2 = 0

Move the constant term to the right:

Add '72.23917197' to each side of the equation.
-72.23917197 + 13r + 72.23917197 + r2 = 0 + 72.23917197

Reorder the terms:
-72.23917197 + 72.23917197 + 13r + r2 = 0 + 72.23917197

Combine like terms: -72.23917197 + 72.23917197 = 0.00000000
0.00000000 + 13r + r2 = 0 + 72.23917197
13r + r2 = 0 + 72.23917197

Combine like terms: 0 + 72.23917197 = 72.23917197
13r + r2 = 72.23917197

The r term is 13r.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13r + 42.25 + r2 = 72.23917197 + 42.25

Reorder the terms:
42.25 + 13r + r2 = 72.23917197 + 42.25

Combine like terms: 72.23917197 + 42.25 = 114.48917197
42.25 + 13r + r2 = 114.48917197

Factor a perfect square on the left side:
(r + 6.5)(r + 6.5) = 114.48917197

Calculate the square root of the right side: 10.699961307

Break this problem into two subproblems by setting 
(r + 6.5) equal to 10.699961307 and -10.699961307.

Subproblem 1

r + 6.5 = 10.699961307 Simplifying r + 6.5 = 10.699961307 Reorder the terms: 6.5 + r = 10.699961307 Solving 6.5 + r = 10.699961307 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + r = 10.699961307 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + r = 10.699961307 + -6.5 r = 10.699961307 + -6.5 Combine like terms: 10.699961307 + -6.5 = 4.199961307 r = 4.199961307 Simplifying r = 4.199961307

Subproblem 2

r + 6.5 = -10.699961307 Simplifying r + 6.5 = -10.699961307 Reorder the terms: 6.5 + r = -10.699961307 Solving 6.5 + r = -10.699961307 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + r = -10.699961307 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + r = -10.699961307 + -6.5 r = -10.699961307 + -6.5 Combine like terms: -10.699961307 + -6.5 = -17.199961307 r = -17.199961307 Simplifying r = -17.199961307

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.199961307, -17.199961307}

See similar equations:

| 7px(3p+4)=-2(2p-1) | | 10x+4-6x-4= | | c^2+2=24 | | b+(a+b)+b+(3a-2b)= | | f(x)=5x^2-3x+3 | | 12n+22=15n+22 | | x-y=5y^2-4x^2 | | -4x+5y-8=0 | | 4w-1=-6w+4 | | 5x^2-20y^2+30x+40y-55=0 | | 2d-6=20 | | 1.50x-4=33.96x | | 3x+7y-5=0 | | 33.96x-4=1.50 | | (a^2+3)=12 | | x+3=2x-19 | | 2x+8=3x-2 | | .16(y-3)+.04y=.02y-2.1 | | 4x-3=2x+5 | | 1.50x=33.96x+4 | | 1.50x=4+33.96x | | 2x^2+24x-148=0 | | 5x=2x-18 | | 3x=15-2x | | 4x-8=x+16 | | x=16-x | | (2x-5y)(3x-7y)= | | 3x+4=8-x | | 2x-6=x+5 | | 2x+4=22-x | | (8x-3)(x+7)= | | 2x=9+x |

Equations solver categories