0=6.28r^2+101.736r-633.024

Simple and best practice solution for 0=6.28r^2+101.736r-633.024 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+101.736r-633.024 equation:


Simplifying
0 = 6.28r2 + 101.736r + -633.024

Reorder the terms:
0 = -633.024 + 101.736r + 6.28r2

Solving
0 = -633.024 + 101.736r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 633.024 = 633.024
633.024 + -101.736r + -6.28r2 = -633.024 + 101.736r + 6.28r2 + 633.024 + -101.736r + -6.28r2

Reorder the terms:
633.024 + -101.736r + -6.28r2 = -633.024 + 633.024 + 101.736r + -101.736r + 6.28r2 + -6.28r2

Combine like terms: -633.024 + 633.024 = 0.000
633.024 + -101.736r + -6.28r2 = 0.000 + 101.736r + -101.736r + 6.28r2 + -6.28r2
633.024 + -101.736r + -6.28r2 = 101.736r + -101.736r + 6.28r2 + -6.28r2

Combine like terms: 101.736r + -101.736r = 0.000
633.024 + -101.736r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
633.024 + -101.736r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
633.024 + -101.736r + -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'.
-100.8 + 16.2r + r2 = 0

Move the constant term to the right:

Add '100.8' to each side of the equation.
-100.8 + 16.2r + 100.8 + r2 = 0 + 100.8

Reorder the terms:
-100.8 + 100.8 + 16.2r + r2 = 0 + 100.8

Combine like terms: -100.8 + 100.8 = 0.0
0.0 + 16.2r + r2 = 0 + 100.8
16.2r + r2 = 0 + 100.8

Combine like terms: 0 + 100.8 = 100.8
16.2r + r2 = 100.8

The r term is 16.2r.  Take half its coefficient (8.1).
Square it (65.61) and add it to both sides.

Add '65.61' to each side of the equation.
16.2r + 65.61 + r2 = 100.8 + 65.61

Reorder the terms:
65.61 + 16.2r + r2 = 100.8 + 65.61

Combine like terms: 100.8 + 65.61 = 166.41
65.61 + 16.2r + r2 = 166.41

Factor a perfect square on the left side:
(r + 8.1)(r + 8.1) = 166.41

Calculate the square root of the right side: 12.9

Break this problem into two subproblems by setting 
(r + 8.1) equal to 12.9 and -12.9.

Subproblem 1

r + 8.1 = 12.9 Simplifying r + 8.1 = 12.9 Reorder the terms: 8.1 + r = 12.9 Solving 8.1 + r = 12.9 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.1' to each side of the equation. 8.1 + -8.1 + r = 12.9 + -8.1 Combine like terms: 8.1 + -8.1 = 0.0 0.0 + r = 12.9 + -8.1 r = 12.9 + -8.1 Combine like terms: 12.9 + -8.1 = 4.8 r = 4.8 Simplifying r = 4.8

Subproblem 2

r + 8.1 = -12.9 Simplifying r + 8.1 = -12.9 Reorder the terms: 8.1 + r = -12.9 Solving 8.1 + r = -12.9 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.1' to each side of the equation. 8.1 + -8.1 + r = -12.9 + -8.1 Combine like terms: 8.1 + -8.1 = 0.0 0.0 + r = -12.9 + -8.1 r = -12.9 + -8.1 Combine like terms: -12.9 + -8.1 = -21 r = -21 Simplifying r = -21

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.8, -21}

See similar equations:

| -32-4x=-5-51+5x | | x*x*X*x+17x+16=0 | | 2y+14=46 | | 6x^2-12x-38=10 | | 3x=1x+300 | | -x+6=25 | | 3x-4=3(x-1)+6 | | 15=-7u+5(u+7) | | 10(2+5y)=270 | | g-g+g-1=13 | | 2x-16y=-18 | | 3x-6=50-5x | | x^2+6x+y^2-8y=0 | | g(5a-2)+3g(2a)ifg(x)=x^2-5x+3 | | 2x-7=18-3x | | f(x)=300(1.16)x | | 11h-4h-6h+2h=9 | | -6x-7=-9x+17 | | 0.66x-1=0.75 | | -10n-n+-20=13 | | 0.7x+20=0.4 | | (4x-2)+(11x+17)= | | 2x-5(x+1)=7 | | X^2+12x+3=7 | | -21+9y=-19 | | 4x-7=65-4x | | 4x-5+2(3x)+17=-2+2x+(16-5) | | 2x(3x-1)=6x-4 | | 3t+0u=30 | | 10y^2-7=74 | | 3t+0u= | | 3x+106+32=180 |

Equations solver categories