25.748=6.28r^2+6.28*r*13

Simple and best practice solution for 25.748=6.28r^2+6.28*r*13 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 25.748=6.28r^2+6.28*r*13 equation: 


Simplifying
25.748 = 6.28r2 + 6.28r * 13

Reorder the terms for easier multiplication:
25.748 = 6.28r2 + 6.28 * 13r

Multiply 6.28 * 13
25.748 = 6.28r2 + 81.64r

Reorder the terms:
25.748 = 81.64r + 6.28r2

Solving
25.748 = 81.64r + 6.28r2

Solving for variable 'r'.

Reorder the terms:
25.748 + -81.64r + -6.28r2 = 81.64r + -81.64r + 6.28r2 + -6.28r2

Combine like terms: 81.64r + -81.64r = 0.00
25.748 + -81.64r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2
25.748 + -81.64r + -6.28r2 = 6.28r2 + -6.28r2

Combine like terms: 6.28r2 + -6.28r2 = 0.00
25.748 + -81.64r + -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'.
-4.1 + 13r + r2 = 0

Move the constant term to the right:

Add '4.1' to each side of the equation.
-4.1 + 13r + 4.1 + r2 = 0 + 4.1

Reorder the terms:
-4.1 + 4.1 + 13r + r2 = 0 + 4.1

Combine like terms: -4.1 + 4.1 = 0.0
0.0 + 13r + r2 = 0 + 4.1
13r + r2 = 0 + 4.1

Combine like terms: 0 + 4.1 = 4.1
13r + r2 = 4.1

The r term is 13r.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13r + 42.25 + r2 = 4.1 + 42.25

Reorder the terms:
42.25 + 13r + r2 = 4.1 + 42.25

Combine like terms: 4.1 + 42.25 = 46.35
42.25 + 13r + r2 = 46.35

Factor a perfect square on the left side:
(r + 6.5)(r + 6.5) = 46.35

Calculate the square root of the right side: 6.808083431

Break this problem into two subproblems by setting 
(r + 6.5) equal to 6.808083431 and -6.808083431.


Subproblem 1
r + 6.5 = 6.808083431

Simplifying
r + 6.5 = 6.808083431

Reorder the terms:
6.5 + r = 6.808083431

Solving
6.5 + r = 6.808083431

Solving for variable 'r'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + r = 6.808083431 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + r = 6.808083431 + -6.5
r = 6.808083431 + -6.5

Combine like terms: 6.808083431 + -6.5 = 0.308083431
r = 0.308083431

Simplifying
r = 0.308083431


Subproblem 2
r + 6.5 = -6.808083431

Simplifying
r + 6.5 = -6.808083431

Reorder the terms:
6.5 + r = -6.808083431

Solving
6.5 + r = -6.808083431

Solving for variable 'r'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + r = -6.808083431 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + r = -6.808083431 + -6.5
r = -6.808083431 + -6.5

Combine like terms: -6.808083431 + -6.5 = -13.308083431
r = -13.308083431

Simplifying
r = -13.308083431


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.308083431, -13.308083431}

See similar equations:

| n^2=24n | | 5-7x=2(3x+6) | | n-6-14= | | .74x=454.73 | | 14x+3+12x+4=85 | | f(x)=-16x^2+15x+10 | | -15s+120=0 | | 3/5÷4/3= | | 3x-20y=369 | | m^4+3m^3=40m^2 | | -3x-27=-12 | | -5(1)=4 | | (t+3)(t-15)= | | 5x+6-8=6x+9-4 | | 3318.1008=6.28r^2+6.28*r*36.5 | | -5(0)=4 | | r^4=.012345679 | | 9x+6+4=3x-2+4 | | 0.7a+2=.25(4a+1) | | 6p-3-5p=4 | | 2010.6048=6.28r^2+6.28*r*36.5 | | 4w^2+9=0 | | 11x-36=8x | | 5p=37-2 | | 12(-8+5t)=384 | | -3+3x=3x+3 | | 3x+8y=154 | | 18(-n)/26 | | 37=5p-2 | | 5(x-3)=86 | | 3x+11=5x+9 | | 5p=37 |

Equations solver categories