9r^2-12r-4=0

Simple and best practice solution for 9r^2-12r-4=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 9r^2-12r-4=0 equation: 


Simplifying
9r2 + -12r + -4 = 0

Reorder the terms:
-4 + -12r + 9r2 = 0

Solving
-4 + -12r + 9r2 = 0

Solving for variable 'r'.

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

Divide each side by '9'.
-0.4444444444 + -1.333333333r + r2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -1.333333333r + 0.4444444444 + r2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -1.333333333r + r2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -1.333333333r + r2 = 0 + 0.4444444444
-1.333333333r + r2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-1.333333333r + r2 = 0.4444444444

The r term is -1.333333333r.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333r + 0.4444444442 + r2 = 0.4444444444 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333r + r2 = 0.4444444444 + 0.4444444442

Combine like terms: 0.4444444444 + 0.4444444442 = 0.8888888886
0.4444444442 + -1.333333333r + r2 = 0.8888888886

Factor a perfect square on the left side:
(r + -0.6666666665)(r + -0.6666666665) = 0.8888888886

Calculate the square root of the right side: 0.942809041

Break this problem into two subproblems by setting 
(r + -0.6666666665) equal to 0.942809041 and -0.942809041.


Subproblem 1
r + -0.6666666665 = 0.942809041

Simplifying
r + -0.6666666665 = 0.942809041

Reorder the terms:
-0.6666666665 + r = 0.942809041

Solving
-0.6666666665 + r = 0.942809041

Solving for variable 'r'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + r = 0.942809041 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + r = 0.942809041 + 0.6666666665
r = 0.942809041 + 0.6666666665

Combine like terms: 0.942809041 + 0.6666666665 = 1.6094757075
r = 1.6094757075

Simplifying
r = 1.6094757075


Subproblem 2
r + -0.6666666665 = -0.942809041

Simplifying
r + -0.6666666665 = -0.942809041

Reorder the terms:
-0.6666666665 + r = -0.942809041

Solving
-0.6666666665 + r = -0.942809041

Solving for variable 'r'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + r = -0.942809041 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + r = -0.942809041 + 0.6666666665
r = -0.942809041 + 0.6666666665

Combine like terms: -0.942809041 + 0.6666666665 = -0.2761423745
r = -0.2761423745

Simplifying
r = -0.2761423745


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.6094757075, -0.2761423745}

See similar equations:

| -16x^2+96x+111=111 | | (5/2w)-12=8 | | x^28=.75 | | 0.85714286(k+8)=24 | | -8=-5+2 | | (x+5)(-x-5)+12.25=0 | | -5n+5=-4n-5 | | 5(4x+2)=40 | | 2r^2+8r+12=r^2 | | 3x-2+2x-7=9 | | 3y-34=142 | | 2(c+3)=18 | | (x^2-2x)(x^2-5)=0 | | 0.857142(k+8)=24 | | 9(x+8)=8x+62 | | 4.5x=270 | | x-6(-4)=-26 | | 6x=18(x^1/2) | | 2y^2+7y-81=0 | | log(52x)=67 | | 3x-2+2x+7=9 | | 1.4x+3y=21 | | -(17+9m)=82 | | (4/5)z=20 | | 15.18=.5x+3.68 | | 12n+-2=46 | | 0=-2x^2+23x+39 | | 3x+9=1x | | Y-4.9=50 | | 8p+2=18 | | -24+1+x=-3+13 | | 3(2x-2)=-18 |

Equations solver categories