0=6.28r^2+404.432r-7009.2336

Simple and best practice solution for 0=6.28r^2+404.432r-7009.2336 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 0=6.28r^2+404.432r-7009.2336 equation:


Simplifying
0 = 6.28r2 + 404.432r + -7009.2336

Reorder the terms:
0 = -7009.2336 + 404.432r + 6.28r2

Solving
0 = -7009.2336 + 404.432r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 7009.2336 = 7009.2336
7009.2336 + -404.432r + -6.28r2 = -7009.2336 + 404.432r + 6.28r2 + 7009.2336 + -404.432r + -6.28r2

Reorder the terms:
7009.2336 + -404.432r + -6.28r2 = -7009.2336 + 7009.2336 + 404.432r + -404.432r + 6.28r2 + -6.28r2

Combine like terms: -7009.2336 + 7009.2336 = 0.0000
7009.2336 + -404.432r + -6.28r2 = 0.0000 + 404.432r + -404.432r + 6.28r2 + -6.28r2
7009.2336 + -404.432r + -6.28r2 = 404.432r + -404.432r + 6.28r2 + -6.28r2

Combine like terms: 404.432r + -404.432r = 0.000
7009.2336 + -404.432r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
7009.2336 + -404.432r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
7009.2336 + -404.432r + -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'.
-1116.12 + 64.4r + r2 = 0

Move the constant term to the right:

Add '1116.12' to each side of the equation.
-1116.12 + 64.4r + 1116.12 + r2 = 0 + 1116.12

Reorder the terms:
-1116.12 + 1116.12 + 64.4r + r2 = 0 + 1116.12

Combine like terms: -1116.12 + 1116.12 = 0.00
0.00 + 64.4r + r2 = 0 + 1116.12
64.4r + r2 = 0 + 1116.12

Combine like terms: 0 + 1116.12 = 1116.12
64.4r + r2 = 1116.12

The r term is 64.4r.  Take half its coefficient (32.2).
Square it (1036.84) and add it to both sides.

Add '1036.84' to each side of the equation.
64.4r + 1036.84 + r2 = 1116.12 + 1036.84

Reorder the terms:
1036.84 + 64.4r + r2 = 1116.12 + 1036.84

Combine like terms: 1116.12 + 1036.84 = 2152.96
1036.84 + 64.4r + r2 = 2152.96

Factor a perfect square on the left side:
(r + 32.2)(r + 32.2) = 2152.96

Calculate the square root of the right side: 46.4

Break this problem into two subproblems by setting 
(r + 32.2) equal to 46.4 and -46.4.

Subproblem 1

r + 32.2 = 46.4 Simplifying r + 32.2 = 46.4 Reorder the terms: 32.2 + r = 46.4 Solving 32.2 + r = 46.4 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-32.2' to each side of the equation. 32.2 + -32.2 + r = 46.4 + -32.2 Combine like terms: 32.2 + -32.2 = 0.0 0.0 + r = 46.4 + -32.2 r = 46.4 + -32.2 Combine like terms: 46.4 + -32.2 = 14.2 r = 14.2 Simplifying r = 14.2

Subproblem 2

r + 32.2 = -46.4 Simplifying r + 32.2 = -46.4 Reorder the terms: 32.2 + r = -46.4 Solving 32.2 + r = -46.4 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-32.2' to each side of the equation. 32.2 + -32.2 + r = -46.4 + -32.2 Combine like terms: 32.2 + -32.2 = 0.0 0.0 + r = -46.4 + -32.2 r = -46.4 + -32.2 Combine like terms: -46.4 + -32.2 = -78.6 r = -78.6 Simplifying r = -78.6

Solution

The solution to the problem is based on the solutions from the subproblems. r = {14.2, -78.6}

See similar equations:

| (3x^3+10x^2+7x-2)/(x-2) | | 6273543843654832v=3745362736366223 | | -4y-5=-17 | | -17=19x+5 | | 10x-3(x-2)=5(3+2x) | | -3/52z=9/20 | | 10=x+2y | | 20x+8y=0 | | 12+6(z-2)=-3z+1 | | F(x)=2x^4-16x^3-9x^2 | | z-295/7=251/6 | | 8x-12=-20 | | 12+6(z-2)=-3z | | 1/6(y+42)-15=-37 | | 9x-3x=-1+7 | | 6=3x-2y | | 9(x+2)=7(4-x) | | 12+log(11x+23)=1 | | 12+6(z-2)=-32+1 | | w=LN(2.846) | | WLN=2.846 | | 1/2y-4=7 | | LnW=2.846 | | 1/2y=11 | | 27.8+(-49-53)= | | 5/6b-6=-18 | | -4(k+4)-(2k-8)=-7k | | -3.24-22.5= | | 10=q-4/1/2 | | 4(x^2-8)=16 | | -w+9=18w-18 | | 35-4x+1= |

Equations solver categories