189.028=2*3.14r^2+2*3.14r*2.7

Simple and best practice solution for 189.028=2*3.14r^2+2*3.14r*2.7 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 189.028=2*3.14r^2+2*3.14r*2.7 equation: 


Simplifying
189.028 = 2 * 3.14r2 + 2 * 3.14r * 2.7

Multiply 2 * 3.14
189.028 = 6.28r2 + 2 * 3.14r * 2.7

Reorder the terms for easier multiplication:
189.028 = 6.28r2 + 2 * 3.14 * 2.7r

Multiply 2 * 3.14
189.028 = 6.28r2 + 6.28 * 2.7r

Multiply 6.28 * 2.7
189.028 = 6.28r2 + 16.956r

Reorder the terms:
189.028 = 16.956r + 6.28r2

Solving
189.028 = 16.956r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
189.028 + -16.956r + -6.28r2 = 16.956r + -16.956r + 6.28r2 + -6.28r2

Combine like terms: 16.956r + -16.956r = 0.000
189.028 + -16.956r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2
189.028 + -16.956r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
189.028 + -16.956r + -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'.
-30.1 + 2.7r + r2 = 0

Move the constant term to the right:

Add '30.1' to each side of the equation.
-30.1 + 2.7r + 30.1 + r2 = 0 + 30.1

Reorder the terms:
-30.1 + 30.1 + 2.7r + r2 = 0 + 30.1

Combine like terms: -30.1 + 30.1 = 0.0
0.0 + 2.7r + r2 = 0 + 30.1
2.7r + r2 = 0 + 30.1

Combine like terms: 0 + 30.1 = 30.1
2.7r + r2 = 30.1

The r term is 2.7r.  Take half its coefficient (1.35).
Square it (1.8225) and add it to both sides.

Add '1.8225' to each side of the equation.
2.7r + 1.8225 + r2 = 30.1 + 1.8225

Reorder the terms:
1.8225 + 2.7r + r2 = 30.1 + 1.8225

Combine like terms: 30.1 + 1.8225 = 31.9225
1.8225 + 2.7r + r2 = 31.9225

Factor a perfect square on the left side:
(r + 1.35)(r + 1.35) = 31.9225

Calculate the square root of the right side: 5.65

Break this problem into two subproblems by setting 
(r + 1.35) equal to 5.65 and -5.65.


Subproblem 1
r + 1.35 = 5.65

Simplifying
r + 1.35 = 5.65

Reorder the terms:
1.35 + r = 5.65

Solving
1.35 + r = 5.65

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1.35' to each side of the equation.
1.35 + -1.35 + r = 5.65 + -1.35

Combine like terms: 1.35 + -1.35 = 0.00
0.00 + r = 5.65 + -1.35
r = 5.65 + -1.35

Combine like terms: 5.65 + -1.35 = 4.3
r = 4.3

Simplifying
r = 4.3


Subproblem 2
r + 1.35 = -5.65

Simplifying
r + 1.35 = -5.65

Reorder the terms:
1.35 + r = -5.65

Solving
1.35 + r = -5.65

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1.35' to each side of the equation.
1.35 + -1.35 + r = -5.65 + -1.35

Combine like terms: 1.35 + -1.35 = 0.00
0.00 + r = -5.65 + -1.35
r = -5.65 + -1.35

Combine like terms: -5.65 + -1.35 = -7
r = -7

Simplifying
r = -7


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.3, -7}

See similar equations:

| 2=-2x-3(-3x+11) | | -2z=-8 | | 4x-73=-6x+47 | | 2=-2x-3(3x+11) | | y^2-4x+4y+8=0 | | 6x^3-8x^2+3x-4=0 | | 5(3x+7)=20 | | 12x-54=90 | | 4x-16=x+17 | | -6x+4(2x+4)=0 | | 40x=35x+25 | | -34-x=-5x+18 | | 2x+(6-x)=3-(x+7) | | 4x-62=-5x+46 | | 2.1x+4.4(x*4)=4925 | | 86+(5x+84)=180 | | 2x-67=-5x+17 | | 3m^2-5m-4=8 | | 5x-47=2x+44 | | 4(2-2x)=-48 | | 3.14(3x^2y)(2xy)=v | | 2(5c+3)-11=6c+3 | | y-59.7=-100 | | 4xty=1 | | ln(x+1)+ln(x+2)=0 | | 7x+13x-1=5(4x+5) | | 2(2x+6)=2(x-3) | | x-36=27-6x | | 3.14(3x^2y)(2xy)= | | 3087.3736=2*3.14r^2+2*3.14r*99.9 | | 3(-4x+8)=-36 | | x^2+25x-54=204 |

Equations solver categories