5r^2-20r-9=0

Simple and best practice solution for 5r^2-20r-9=0 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 5r^2-20r-9=0 equation: 


Simplifying
5r2 + -20r + -9 = 0

Reorder the terms:
-9 + -20r + 5r2 = 0

Solving
-9 + -20r + 5r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-1.8 + -4r + r2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -4r + 1.8 + r2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -4r + r2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -4r + r2 = 0 + 1.8
-4r + r2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
-4r + r2 = 1.8

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = 1.8 + 4

Reorder the terms:
4 + -4r + r2 = 1.8 + 4

Combine like terms: 1.8 + 4 = 5.8
4 + -4r + r2 = 5.8

Factor a perfect square on the left side:
(r + -2)(r + -2) = 5.8

Calculate the square root of the right side: 2.408318916

Break this problem into two subproblems by setting 
(r + -2) equal to 2.408318916 and -2.408318916.


Subproblem 1
r + -2 = 2.408318916

Simplifying
r + -2 = 2.408318916

Reorder the terms:
-2 + r = 2.408318916

Solving
-2 + r = 2.408318916

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = 2.408318916 + 2

Combine like terms: -2 + 2 = 0
0 + r = 2.408318916 + 2
r = 2.408318916 + 2

Combine like terms: 2.408318916 + 2 = 4.408318916
r = 4.408318916

Simplifying
r = 4.408318916


Subproblem 2
r + -2 = -2.408318916

Simplifying
r + -2 = -2.408318916

Reorder the terms:
-2 + r = -2.408318916

Solving
-2 + r = -2.408318916

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = -2.408318916 + 2

Combine like terms: -2 + 2 = 0
0 + r = -2.408318916 + 2
r = -2.408318916 + 2

Combine like terms: -2.408318916 + 2 = -0.408318916
r = -0.408318916

Simplifying
r = -0.408318916


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.408318916, -0.408318916}

See similar equations:

| 13.62+.13(x+3)=14.37-.09x | | xsquare(x+5)(x-5)=0 | | 1600x=20 | | 3y+17=62 | | y+19=192 | | f(-6)=7-2x | | 4x+14=5x | | 2x=6(2x-2)-5 | | 13.62+.13(x+3)=14.37+.09x | | 3(3+1)=(9-2x) | | 6n=(n+5) | | 30=-8x+2(x-6) | | y=mx+bfindx | | x^1/4=2 | | 5x-15=2x+20 | | 90+3+x+x-8=180 | | 10n-0.75=0.1n-0.375 | | 2-7g=2-g | | 2e^3x-9=0 | | 12a=3a+2.5a+a | | -1=6x-31 | | 15.93+.09(x+3)=16.43-.13x | | -3(3y-7)+2(2y+8)= | | 2[-2(4x+5)+4(3x-4)]= | | z/3=11 | | 5x-7=2x-14 | | 7/3.7/5 | | 51=50 | | (x/3)-9= | | -7y-12w=29 | | (-3/7)÷(-14/11) | | -5y-8=-3y+2 |

Equations solver categories