742.61=2*3.14*r^2+2*3.14*r*16

Simple and best practice solution for 742.61=2*3.14*r^2+2*3.14*r*16 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 742.61=2*3.14*r^2+2*3.14*r*16 equation:


Simplifying
742.61 = 2 * 3.14r2 + 2 * 3.14r * 16

Multiply 2 * 3.14
742.61 = 6.28r2 + 2 * 3.14r * 16

Reorder the terms for easier multiplication:
742.61 = 6.28r2 + 2 * 3.14 * 16r

Multiply 2 * 3.14
742.61 = 6.28r2 + 6.28 * 16r

Multiply 6.28 * 16
742.61 = 6.28r2 + 100.48r

Reorder the terms:
742.61 = 100.48r + 6.28r2

Solving
742.61 = 100.48r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
742.61 + -100.48r + -6.28r2 = 100.48r + -100.48r + 6.28r2 + -6.28r2

Combine like terms: 100.48r + -100.48r = 0.00
742.61 + -100.48r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
742.61 + -100.48r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
742.61 + -100.48r + -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'.
-118.25 + 16r + r2 = 0

Move the constant term to the right:

Add '118.25' to each side of the equation.
-118.25 + 16r + 118.25 + r2 = 0 + 118.25

Reorder the terms:
-118.25 + 118.25 + 16r + r2 = 0 + 118.25

Combine like terms: -118.25 + 118.25 = 0.00
0.00 + 16r + r2 = 0 + 118.25
16r + r2 = 0 + 118.25

Combine like terms: 0 + 118.25 = 118.25
16r + r2 = 118.25

The r term is 16r.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16r + 64 + r2 = 118.25 + 64

Reorder the terms:
64 + 16r + r2 = 118.25 + 64

Combine like terms: 118.25 + 64 = 182.25
64 + 16r + r2 = 182.25

Factor a perfect square on the left side:
(r + 8)(r + 8) = 182.25

Calculate the square root of the right side: 13.5

Break this problem into two subproblems by setting 
(r + 8) equal to 13.5 and -13.5.

Subproblem 1

r + 8 = 13.5 Simplifying r + 8 = 13.5 Reorder the terms: 8 + r = 13.5 Solving 8 + r = 13.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 13.5 + -8 Combine like terms: 8 + -8 = 0 0 + r = 13.5 + -8 r = 13.5 + -8 Combine like terms: 13.5 + -8 = 5.5 r = 5.5 Simplifying r = 5.5

Subproblem 2

r + 8 = -13.5 Simplifying r + 8 = -13.5 Reorder the terms: 8 + r = -13.5 Solving 8 + r = -13.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -13.5 + -8 Combine like terms: 8 + -8 = 0 0 + r = -13.5 + -8 r = -13.5 + -8 Combine like terms: -13.5 + -8 = -21.5 r = -21.5 Simplifying r = -21.5

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.5, -21.5}

See similar equations:

| 13y=78 | | 5(w+7)=-5(2w-5)+3w | | 3+5x=103 | | b+43=34 | | 982893x+20823023=2323 | | 4x-9x^2=0 | | z^2+7x-3=0 | | (c-1)(c+2)=14 | | 3y+16=-11+6y | | 8r^2+30r-27=0 | | 6.8-5.27= | | -3(-3w+8)-9w=6(w-6)-2 | | 2m+40=10 | | j+29=57 | | 7x-11=6x+12 | | (1.2)(0.06)= | | (x-1)(x+2)=14 | | (l^2-4)x^4+l(l-2)x^3+3lx^2+5lx-2l= | | 3n^2+31n+56=0 | | 16(sin^2)(x)=1 | | 7+2(7u-4)=-2(4u-1)+4u | | 7b^2+71b+72=0 | | x^4-x^2=600 | | Y=100(1.025) | | 4y-4=2y+2 | | 5b^2+44b-9=0 | | 11v-3v=32 | | 4+2c=6 | | F(-5)=4(-5)-3 | | v=b+(a)(t) | | 3m^2+7m-10=0 | | 8x-7+2x=6x-1 |

Equations solver categories