3x^2+2x=9

Simple and best practice solution for 3x^2+2x=9 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 3x^2+2x=9 equation:


Simplifying
3x2 + 2x = 9

Reorder the terms:
2x + 3x2 = 9

Solving
2x + 3x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 2x + 3x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 2x + 3x2 = 0

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

Divide each side by '3'.
-3 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 0.6666666667x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 0.6666666667x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 0.6666666667x + x2 = 0 + 3
0.6666666667x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
0.6666666667x + x2 = 3

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 3 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 3 + 0.1111111112

Combine like terms: 3 + 0.1111111112 = 3.1111111112
0.1111111112 + 0.6666666667x + x2 = 3.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 3.1111111112

Calculate the square root of the right side: 1.763834207

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.763834207 and -1.763834207.

Subproblem 1

x + 0.3333333334 = 1.763834207 Simplifying x + 0.3333333334 = 1.763834207 Reorder the terms: 0.3333333334 + x = 1.763834207 Solving 0.3333333334 + x = 1.763834207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.763834207 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.763834207 + -0.3333333334 x = 1.763834207 + -0.3333333334 Combine like terms: 1.763834207 + -0.3333333334 = 1.4305008736 x = 1.4305008736 Simplifying x = 1.4305008736

Subproblem 2

x + 0.3333333334 = -1.763834207 Simplifying x + 0.3333333334 = -1.763834207 Reorder the terms: 0.3333333334 + x = -1.763834207 Solving 0.3333333334 + x = -1.763834207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.763834207 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.763834207 + -0.3333333334 x = -1.763834207 + -0.3333333334 Combine like terms: -1.763834207 + -0.3333333334 = -2.0971675404 x = -2.0971675404 Simplifying x = -2.0971675404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4305008736, -2.0971675404}

See similar equations:

| 0.5=c+6.1 | | m^2-28m=39 | | 7x+6=-5y | | 6x^2=216x | | c+-3=-6.2 | | 2m^2+9m-30=5 | | 2n^2+4n-30= | | 11t+8t=15 | | 3x*62345=5x+65 | | y^2-20y+27=0 | | 5.8=5.7 | | -2q^2-28q=-86 | | n-1.4=7.5 | | P=45x+48y | | 7x^2+3=7-40x | | 3y+4(x+t)= | | -8.9=n+-6.5 | | 7v^2+10v+3=0 | | 16x^6-81x^2=0 | | 3.5a-a= | | 3x-4=12x+23 | | 3x+4(3x-5)=10 | | 9x+20+6x-3+83-5x=180 | | -3=p+0.8 | | 9x+20+6x-3+83-5x=1801 | | Ln(0.5x+3)=6 | | 6k^2-k-2=0 | | c+4.3=5.8 | | 30=log(x) | | c+-0.8=-3.6 | | g^2+14g=-45 | | -4x-1/4=c |

Equations solver categories