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 = 0.2761423745
r = 0.2761423745

Simplifying
r = 0.2761423745


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 = -1.6094757075
r = -1.6094757075

Simplifying
r = -1.6094757075


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

See similar equations:

| -y=2(0)-8 | | -y=2(2)-8 | | 215-5x=31x+19 | | 15(-2)-16=5y+9 | | 3/4(20a+12)+1/4(20a+12) | | 5-(x+6)=0 | | 15(0)-16=5y+9 | | 15(2)-16=5y+9 | | 5x+23=14x-23 | | 3x+8y=16 | | 0=-7 | | 5c/9c^6 | | 2=-7 | | f(10)=50-2x | | -7x-3=9 | | -7x-3=19 | | 10-7x=1+2x | | -7x-3=10 | | m+8.5=13.7 | | 16=8(-2)-4y | | 16=8(0)-4y | | 15a=6a+108 | | 5p-2p+4p= | | 16=8(2)-4y | | y=2*-1+(-2) | | 0=3 | | 60=3w^2 | | -(-2)-2=y | | -(0)-2=y | | 3x-6=4(6+3x) | | -(2)-2=y | | 2x+3y=130 |

Equations solver categories