16616.88=6.28*r^2+6.28*r*105

Simple and best practice solution for 16616.88=6.28*r^2+6.28*r*105 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 16616.88=6.28*r^2+6.28*r*105 equation:


Simplifying
16616.88 = 6.28r2 + 6.28r * 105

Reorder the terms for easier multiplication:
16616.88 = 6.28r2 + 6.28 * 105r

Multiply 6.28 * 105
16616.88 = 6.28r2 + 659.4r

Reorder the terms:
16616.88 = 659.4r + 6.28r2

Solving
16616.88 = 659.4r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
16616.88 + -659.4r + -6.28r2 = 659.4r + -659.4r + 6.28r2 + -6.28r2

Combine like terms: 659.4r + -659.4r = 0.0
16616.88 + -659.4r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2
16616.88 + -659.4r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
16616.88 + -659.4r + -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'.
-2646 + 105r + r2 = 0

Move the constant term to the right:

Add '2646' to each side of the equation.
-2646 + 105r + 2646 + r2 = 0 + 2646

Reorder the terms:
-2646 + 2646 + 105r + r2 = 0 + 2646

Combine like terms: -2646 + 2646 = 0
0 + 105r + r2 = 0 + 2646
105r + r2 = 0 + 2646

Combine like terms: 0 + 2646 = 2646
105r + r2 = 2646

The r term is 105r.  Take half its coefficient (52.5).
Square it (2756.25) and add it to both sides.

Add '2756.25' to each side of the equation.
105r + 2756.25 + r2 = 2646 + 2756.25

Reorder the terms:
2756.25 + 105r + r2 = 2646 + 2756.25

Combine like terms: 2646 + 2756.25 = 5402.25
2756.25 + 105r + r2 = 5402.25

Factor a perfect square on the left side:
(r + 52.5)(r + 52.5) = 5402.25

Calculate the square root of the right side: 73.5

Break this problem into two subproblems by setting 
(r + 52.5) equal to 73.5 and -73.5.

Subproblem 1

r + 52.5 = 73.5 Simplifying r + 52.5 = 73.5 Reorder the terms: 52.5 + r = 73.5 Solving 52.5 + r = 73.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + r = 73.5 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + r = 73.5 + -52.5 r = 73.5 + -52.5 Combine like terms: 73.5 + -52.5 = 21 r = 21 Simplifying r = 21

Subproblem 2

r + 52.5 = -73.5 Simplifying r + 52.5 = -73.5 Reorder the terms: 52.5 + r = -73.5 Solving 52.5 + r = -73.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + r = -73.5 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + r = -73.5 + -52.5 r = -73.5 + -52.5 Combine like terms: -73.5 + -52.5 = -126 r = -126 Simplifying r = -126

Solution

The solution to the problem is based on the solutions from the subproblems. r = {21, -126}

See similar equations:

| 9=8m | | z+81=9z+-7 | | y=300+10x | | 9(4+5*9)= | | 3t(t-1)=60 | | 9(x+5y)=0 | | 6x+4x+3+6=7x+3+2x | | 0.8n=5 | | -8x=24y | | 9x^2+2x+8=0 | | 50y^3-60y^2+18y= | | 9a^3-24a+16= | | 14x-1=3x+1 | | 5x^9y^7+30x^7y^6+35xy=0 | | c^2+8c+7=0 | | 21a^2+39a-6= | | 4(4+-8y)-y=3y+7 | | 10x+y=300 | | -12x^2=0 | | (5b-7)-2(2b+3)=-6 | | x^2+34x+37= | | v^2+4vp-32p^2=0 | | 4b^2+2b=0 | | 6.50-x=5x*50 | | 7x-35=16 | | 7x-35=17 | | xy-3x-4y+12= | | y^2=41 | | 4*x^2-18*x+21=0 | | f(x)=4x^2-5x | | 8x+2=10x+8 | | 21.5*4= |

Equations solver categories