0=6.28r^2+626.116r-3150.048

Simple and best practice solution for 0=6.28r^2+626.116r-3150.048 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+626.116r-3150.048 equation:


Simplifying
0 = 6.28r2 + 626.116r + -3150.048

Reorder the terms:
0 = -3150.048 + 626.116r + 6.28r2

Solving
0 = -3150.048 + 626.116r + 6.28r2

Solving for variable 'r'.

Combine like terms: 0 + 3150.048 = 3150.048
3150.048 + -626.116r + -6.28r2 = -3150.048 + 626.116r + 6.28r2 + 3150.048 + -626.116r + -6.28r2

Reorder the terms:
3150.048 + -626.116r + -6.28r2 = -3150.048 + 3150.048 + 626.116r + -626.116r + 6.28r2 + -6.28r2

Combine like terms: -3150.048 + 3150.048 = 0.000
3150.048 + -626.116r + -6.28r2 = 0.000 + 626.116r + -626.116r + 6.28r2 + -6.28r2
3150.048 + -626.116r + -6.28r2 = 626.116r + -626.116r + 6.28r2 + -6.28r2

Combine like terms: 626.116r + -626.116r = 0.000
3150.048 + -626.116r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
3150.048 + -626.116r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
3150.048 + -626.116r + -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'.
-501.6 + 99.7r + r2 = 0

Move the constant term to the right:

Add '501.6' to each side of the equation.
-501.6 + 99.7r + 501.6 + r2 = 0 + 501.6

Reorder the terms:
-501.6 + 501.6 + 99.7r + r2 = 0 + 501.6

Combine like terms: -501.6 + 501.6 = 0.0
0.0 + 99.7r + r2 = 0 + 501.6
99.7r + r2 = 0 + 501.6

Combine like terms: 0 + 501.6 = 501.6
99.7r + r2 = 501.6

The r term is 99.7r.  Take half its coefficient (49.85).
Square it (2485.0225) and add it to both sides.

Add '2485.0225' to each side of the equation.
99.7r + 2485.0225 + r2 = 501.6 + 2485.0225

Reorder the terms:
2485.0225 + 99.7r + r2 = 501.6 + 2485.0225

Combine like terms: 501.6 + 2485.0225 = 2986.6225
2485.0225 + 99.7r + r2 = 2986.6225

Factor a perfect square on the left side:
(r + 49.85)(r + 49.85) = 2986.6225

Calculate the square root of the right side: 54.65

Break this problem into two subproblems by setting 
(r + 49.85) equal to 54.65 and -54.65.

Subproblem 1

r + 49.85 = 54.65 Simplifying r + 49.85 = 54.65 Reorder the terms: 49.85 + r = 54.65 Solving 49.85 + r = 54.65 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-49.85' to each side of the equation. 49.85 + -49.85 + r = 54.65 + -49.85 Combine like terms: 49.85 + -49.85 = 0.00 0.00 + r = 54.65 + -49.85 r = 54.65 + -49.85 Combine like terms: 54.65 + -49.85 = 4.8 r = 4.8 Simplifying r = 4.8

Subproblem 2

r + 49.85 = -54.65 Simplifying r + 49.85 = -54.65 Reorder the terms: 49.85 + r = -54.65 Solving 49.85 + r = -54.65 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-49.85' to each side of the equation. 49.85 + -49.85 + r = -54.65 + -49.85 Combine like terms: 49.85 + -49.85 = 0.00 0.00 + r = -54.65 + -49.85 r = -54.65 + -49.85 Combine like terms: -54.65 + -49.85 = -104.5 r = -104.5 Simplifying r = -104.5

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.8, -104.5}

See similar equations:

| 8b^2-280=16b | | 72(x)=2.25(x)+26.25 | | 10x^2+11x-1110=0 | | 42-y=2 | | 10logx=10 | | 3n-5=4n | | 216=x(15+x) | | 3t^3+t^2=0 | | 2.5(10x-3)=16x+15 | | x+5*2=23 | | h(19.4)=2.25(19.4)+26.25 | | (m+2)(4m+5)=0 | | 5(x+2)-7=33 | | -5-0.375x=x | | 6t^2-4t-2=0 | | 3052=(1/3)*3.14*r^3 | | 2x+y=1400 | | 8x+13=5x+25 | | 3052=(4/3)*3.14*r^3 | | h(-0.5)=0.25 | | 16/(4-2)*3 | | 2x^2+-1=0 | | (n-1)(n-3)=0 | | 16/(4-2)x3 | | 3052=4/3*3.14*r^3 | | (p+5)(p+3)=0 | | x+5x+3x=38 | | 4(x-3)+25=0 | | 3/5=x/42 | | (3n-5)(n-3)=0 | | 8x^2+11x-13=0 | | X/8=60/96 |

Equations solver categories