0=6.28r^2+384.336r-6611.584

Simple and best practice solution for 0=6.28r^2+384.336r-6611.584 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+384.336r-6611.584 equation:


Simplifying
0 = 6.28r2 + 384.336r + -6611.584

Reorder the terms:
0 = -6611.584 + 384.336r + 6.28r2

Solving
0 = -6611.584 + 384.336r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 6611.584 = 6611.584
6611.584 + -384.336r + -6.28r2 = -6611.584 + 384.336r + 6.28r2 + 6611.584 + -384.336r + -6.28r2

Reorder the terms:
6611.584 + -384.336r + -6.28r2 = -6611.584 + 6611.584 + 384.336r + -384.336r + 6.28r2 + -6.28r2

Combine like terms: -6611.584 + 6611.584 = 0.000
6611.584 + -384.336r + -6.28r2 = 0.000 + 384.336r + -384.336r + 6.28r2 + -6.28r2
6611.584 + -384.336r + -6.28r2 = 384.336r + -384.336r + 6.28r2 + -6.28r2

Combine like terms: 384.336r + -384.336r = 0.000
6611.584 + -384.336r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
6611.584 + -384.336r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
6611.584 + -384.336r + -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'.
-1052.8 + 61.2r + r2 = 0

Move the constant term to the right:

Add '1052.8' to each side of the equation.
-1052.8 + 61.2r + 1052.8 + r2 = 0 + 1052.8

Reorder the terms:
-1052.8 + 1052.8 + 61.2r + r2 = 0 + 1052.8

Combine like terms: -1052.8 + 1052.8 = 0.0
0.0 + 61.2r + r2 = 0 + 1052.8
61.2r + r2 = 0 + 1052.8

Combine like terms: 0 + 1052.8 = 1052.8
61.2r + r2 = 1052.8

The r term is 61.2r.  Take half its coefficient (30.6).
Square it (936.36) and add it to both sides.

Add '936.36' to each side of the equation.
61.2r + 936.36 + r2 = 1052.8 + 936.36

Reorder the terms:
936.36 + 61.2r + r2 = 1052.8 + 936.36

Combine like terms: 1052.8 + 936.36 = 1989.16
936.36 + 61.2r + r2 = 1989.16

Factor a perfect square on the left side:
(r + 30.6)(r + 30.6) = 1989.16

Calculate the square root of the right side: 44.6

Break this problem into two subproblems by setting 
(r + 30.6) equal to 44.6 and -44.6.

Subproblem 1

r + 30.6 = 44.6 Simplifying r + 30.6 = 44.6 Reorder the terms: 30.6 + r = 44.6 Solving 30.6 + r = 44.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-30.6' to each side of the equation. 30.6 + -30.6 + r = 44.6 + -30.6 Combine like terms: 30.6 + -30.6 = 0.0 0.0 + r = 44.6 + -30.6 r = 44.6 + -30.6 Combine like terms: 44.6 + -30.6 = 14 r = 14 Simplifying r = 14

Subproblem 2

r + 30.6 = -44.6 Simplifying r + 30.6 = -44.6 Reorder the terms: 30.6 + r = -44.6 Solving 30.6 + r = -44.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-30.6' to each side of the equation. 30.6 + -30.6 + r = -44.6 + -30.6 Combine like terms: 30.6 + -30.6 = 0.0 0.0 + r = -44.6 + -30.6 r = -44.6 + -30.6 Combine like terms: -44.6 + -30.6 = -75.2 r = -75.2 Simplifying r = -75.2

Solution

The solution to the problem is based on the solutions from the subproblems. r = {14, -75.2}

See similar equations:

| 20x+24=12x | | 60c+-39=21 | | 2x-8=4x+6 | | 6b^2-25b+4=0 | | 4m^2-3=-4 | | ln(x)-ln(x+7)=ln(4x-28) | | f(x)=4x^4-15x^3+5x^2+15x-9 | | 654+654x=748425489 | | -8f=-80 | | 8y=5y | | 34w-5w-10w-7=88 | | -3x+4=2x | | 15n-14+2n-2n-1=18 | | 7c=14 | | ln(x)=22 | | 2(3(x-1))+x=1 | | X^2-14x-14=0 | | 4(c-14)+-2=14 | | -8n+(1+5n)=-614 | | 3(c-24)=6 | | ln(5x^2+2)-x=0 | | .4n+2=2n+3.2 | | -g+13g+9=-15 | | 3D+8+2d-7=26 | | 30x^2-38x+12=20x^2-14x+2 | | 8x+7+2x+6= | | x(x+8)=(x+5)(2x-8) | | (x+1)(7x)= | | .75(8b+4)-1=4b+14 | | 7x-4y+2x-1-3y= | | a*a-17a+16=0 | | 6x^2-12x=8 |

Equations solver categories