9x^2+12x-9=0

Simple and best practice solution for 9x^2+12x-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 9x^2+12x-9=0 equation: 


Simplifying
9x2 + 12x + -9 = 0

Reorder the terms:
-9 + 12x + 9x2 = 0

Solving
-9 + 12x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 4x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + 4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-3 + 4x + 3x2 = 0

Solving
-3 + 4x + 3x2 = 0

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

Divide each side by '3'.
-1 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.333333333x + x2 = 0 + 1
1.333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.333333333x + x2 = 1

The x term is 1.333333333x.  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.
1.333333333x + 0.4444444442 + x2 = 1 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 1 + 0.4444444442

Combine like terms: 1 + 0.4444444442 = 1.4444444442
0.4444444442 + 1.333333333x + x2 = 1.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 1.4444444442

Calculate the square root of the right side: 1.201850425

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.201850425 and -1.201850425.


Subproblem 1
x + 0.6666666665 = 1.201850425

Simplifying
x + 0.6666666665 = 1.201850425

Reorder the terms:
0.6666666665 + x = 1.201850425

Solving
0.6666666665 + x = 1.201850425

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 1.201850425 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 1.201850425 + -0.6666666665
x = 1.201850425 + -0.6666666665

Combine like terms: 1.201850425 + -0.6666666665 = 0.5351837585
x = 0.5351837585

Simplifying
x = 0.5351837585


Subproblem 2
x + 0.6666666665 = -1.201850425

Simplifying
x + 0.6666666665 = -1.201850425

Reorder the terms:
0.6666666665 + x = -1.201850425

Solving
0.6666666665 + x = -1.201850425

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -1.201850425 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -1.201850425 + -0.6666666665
x = -1.201850425 + -0.6666666665

Combine like terms: -1.201850425 + -0.6666666665 = -1.8685170915
x = -1.8685170915

Simplifying
x = -1.8685170915


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5351837585, -1.8685170915}
Solution
x = {0.5351837585, -1.8685170915}

See similar equations:

| 10x+8y=48 | | 3(x-6)=99/11 | | -26x^2/35/39x/-40 | | 1-5x=-19 | | abs(x)-6=0 | | 7x-1=-43 | | abs(3y+15)=24 | | 7y-20=-6 | | x^2+9=19 | | 81a^2-16b^2=0 | | x^2+5x=-11 | | x^2+5=174 | | x/5-2=18 | | -33+15=-18 | | z/5+60=45 | | 4y^2-7y-2=0 | | 20+4t=5(t+5) | | 9x^2+12xy+4y^2=0 | | -4+10=17x-5-16x | | 64p^3+125=0 | | -3x-5=2x-2 | | 25x-100=-150 | | 27m^3+125=0 | | 81g^2-16g^2=0 | | 81g^2-16r^2=0 | | 8-y=21 | | 6-4x=x | | 36x^2+84xy+49y^2=0 | | 4(3c-1)-2=9c+3 | | 25a^2-70a+49= | | 4/7z=12 | | 5/6n=20 |

Equations solver categories