6x^2+9x+2=0

Simple and best practice solution for 6x^2+9x+2=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 6x^2+9x+2=0 equation:


Simplifying
6x2 + 9x + 2 = 0

Reorder the terms:
2 + 9x + 6x2 = 0

Solving
2 + 9x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
0.3333333333 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 1.5x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 1.5x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 1.5x + x2 = 0 + -0.3333333333
1.5x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
1.5x + x2 = -0.3333333333

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -0.3333333333 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -0.3333333333 + 0.5625

Combine like terms: -0.3333333333 + 0.5625 = 0.2291666667
0.5625 + 1.5x + x2 = 0.2291666667

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.2291666667

Calculate the square root of the right side: 0.478713554

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.478713554 and -0.478713554.

Subproblem 1

x + 0.75 = 0.478713554 Simplifying x + 0.75 = 0.478713554 Reorder the terms: 0.75 + x = 0.478713554 Solving 0.75 + x = 0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.478713554 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.478713554 + -0.75 x = 0.478713554 + -0.75 Combine like terms: 0.478713554 + -0.75 = -0.271286446 x = -0.271286446 Simplifying x = -0.271286446

Subproblem 2

x + 0.75 = -0.478713554 Simplifying x + 0.75 = -0.478713554 Reorder the terms: 0.75 + x = -0.478713554 Solving 0.75 + x = -0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -0.478713554 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.478713554 + -0.75 x = -0.478713554 + -0.75 Combine like terms: -0.478713554 + -0.75 = -1.228713554 x = -1.228713554 Simplifying x = -1.228713554

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.271286446, -1.228713554}

See similar equations:

| -6(2b+1)+(13b-4)=0 | | 3(x+5)=33+x | | n^2-n-132=0 | | m-4.8=12.13 | | 6.4x-1=5.4x | | 4x^2-20x=0 | | (x+3)(x+2)=(2x+16)(x-1) | | (-3)-6x=(-21) | | 4x^2-49=0 | | 5x^4+17x^3+6x^2=0 | | 3x^2+11x+4=0 | | 3x^2+11x-4=0 | | (x+5)(x+3)(2x-1)=0 | | -3(7p+2)-2(6-14p)=3(6+2p) | | 100y^2+160y+128=0 | | 7y=9y-8 | | 3x+83=8x+8 | | 2.5x+15y=8.75 | | 0.5x+3y=1.75 | | 3+2y=5 | | a-b-c-d-e-f-g-h=k | | 7.5x+6y=8.25 | | c-d-c-d-e-f-g=o | | 2.5x+2y=2.75 | | 3x+12y=19.5 | | 0.5x+2y=3.25 | | y^2-13y+44=0 | | 5+-9=26 | | 14x+2+11x+3=180 | | 12x+1+7x+8=180 | | 0=-2m+8 | | s^4+2s^3-25s^2-50s=0 |

Equations solver categories