4148.9448=2*3.14*r^2+2*3.14*r+42.5

Simple and best practice solution for 4148.9448=2*3.14*r^2+2*3.14*r+42.5 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 4148.9448=2*3.14*r^2+2*3.14*r+42.5 equation:


Simplifying
4148.9448 = 2 * 3.14r2 + 2 * 3.14r + 42.5

Multiply 2 * 3.14
4148.9448 = 6.28r2 + 2 * 3.14r + 42.5

Multiply 2 * 3.14
4148.9448 = 6.28r2 + 6.28r + 42.5

Reorder the terms:
4148.9448 = 42.5 + 6.28r + 6.28r2

Solving
4148.9448 = 42.5 + 6.28r + 6.28r2

Solving for variable 'r'.

Combine like terms: 4148.9448 + -42.5 = 4106.4448
4106.4448 + -6.28r + -6.28r2 = 42.5 + 6.28r + 6.28r2 + -42.5 + -6.28r + -6.28r2

Reorder the terms:
4106.4448 + -6.28r + -6.28r2 = 42.5 + -42.5 + 6.28r + -6.28r + 6.28r2 + -6.28r2

Combine like terms: 42.5 + -42.5 = 0.0
4106.4448 + -6.28r + -6.28r2 = 0.0 + 6.28r + -6.28r + 6.28r2 + -6.28r2
4106.4448 + -6.28r + -6.28r2 = 6.28r + -6.28r + 6.28r2 + -6.28r2

Combine like terms: 6.28r + -6.28r = 0.00
4106.4448 + -6.28r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
4106.4448 + -6.28r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
4106.4448 + -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'.
-653.8924841 + r + r2 = 0

Move the constant term to the right:

Add '653.8924841' to each side of the equation.
-653.8924841 + r + 653.8924841 + r2 = 0 + 653.8924841

Reorder the terms:
-653.8924841 + 653.8924841 + r + r2 = 0 + 653.8924841

Combine like terms: -653.8924841 + 653.8924841 = 0.0000000
0.0000000 + r + r2 = 0 + 653.8924841
r + r2 = 0 + 653.8924841

Combine like terms: 0 + 653.8924841 = 653.8924841
r + r2 = 653.8924841

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 = 653.8924841 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + r2 = 653.8924841 + 0.25

Combine like terms: 653.8924841 + 0.25 = 654.1424841
1.25 + r2 = 654.1424841

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 654.1424841

Calculate the square root of the right side: 25.576209338

Break this problem into two subproblems by setting 
(r + 0.5) equal to 25.576209338 and -25.576209338.

Subproblem 1

r + 0.5 = 25.576209338 Simplifying r + 0.5 = 25.576209338 Reorder the terms: 0.5 + r = 25.576209338 Solving 0.5 + r = 25.576209338 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 = 25.576209338 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 25.576209338 + -0.5 r = 25.576209338 + -0.5 Combine like terms: 25.576209338 + -0.5 = 25.076209338 r = 25.076209338 Simplifying r = 25.076209338

Subproblem 2

r + 0.5 = -25.576209338 Simplifying r + 0.5 = -25.576209338 Reorder the terms: 0.5 + r = -25.576209338 Solving 0.5 + r = -25.576209338 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 = -25.576209338 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -25.576209338 + -0.5 r = -25.576209338 + -0.5 Combine like terms: -25.576209338 + -0.5 = -26.076209338 r = -26.076209338 Simplifying r = -26.076209338

Solution

The solution to the problem is based on the solutions from the subproblems. r = {25.076209338, -26.076209338}

See similar equations:

| 4x+2(-4x-4)=16 | | 3x^2=2025 | | 3x^3=2025 | | x^2+16=-8 | | -[2z-(5z+1)]=1+(2z+2) | | 33x=445.5 | | 2x^2+50-49=0 | | O=-3+12-9n | | 0.07=mx+40 | | (6X+11)+(2X+13)= | | =2+5n-5 | | 5x^4+10x^2+1=0 | | Y=0.07x+40 | | X-10+3h+4+2h+x= | | y^1+2xy=4x | | 3x^2=4x^2 | | 21y-8(2)=6y+1-10 | | 550.8816=2*3.14*r^2+2*3.14*r^2*16.1 | | .4x+5.2=3.8 | | 8x+9y=540 | | 2x-3-9x=14+x+1 | | 3x-4(4-2x)=4 | | 56b^2-17b-3= | | 4*e=17 | | 3x-16+8x=4 | | 24x^4-14x^2-3=0 | | 7x^2-5r-8=-8 | | -3x+3(-x-3)=81 | | e-14=8 | | -5(2x-7)+24=29 | | 7+x+3x=6x-1 | | 4x-2(-4x-5)=82 |

Equations solver categories