6x^2+33x+18=0

Simple and best practice solution for 6x^2+33x+18=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+33x+18=0 equation: 


Simplifying
6x2 + 33x + 18 = 0

Reorder the terms:
18 + 33x + 6x2 = 0

Solving
18 + 33x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 11x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(6 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
6 + 11x + 2x2 = 0

Solving
6 + 11x + 2x2 = 0

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

Divide each side by '2'.
3 + 5.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 5.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5.5x + x2 = 0 + -3
5.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
5.5x + x2 = -3

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = -3 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -3 + 7.5625

Combine like terms: -3 + 7.5625 = 4.5625
7.5625 + 5.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + 2.75) equal to 2.136000936 and -2.136000936.


Subproblem 1
x + 2.75 = 2.136000936

Simplifying
x + 2.75 = 2.136000936

Reorder the terms:
2.75 + x = 2.136000936

Solving
2.75 + x = 2.136000936

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 2.136000936 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 2.136000936 + -2.75
x = 2.136000936 + -2.75

Combine like terms: 2.136000936 + -2.75 = -0.613999064
x = -0.613999064

Simplifying
x = -0.613999064


Subproblem 2
x + 2.75 = -2.136000936

Simplifying
x + 2.75 = -2.136000936

Reorder the terms:
2.75 + x = -2.136000936

Solving
2.75 + x = -2.136000936

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -2.136000936 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -2.136000936 + -2.75
x = -2.136000936 + -2.75

Combine like terms: -2.136000936 + -2.75 = -4.886000936
x = -4.886000936

Simplifying
x = -4.886000936


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.613999064, -4.886000936}
Solution
x = {-0.613999064, -4.886000936}

See similar equations:

| 3x^2-24x+x+2=0 | | x^2+6x-39=0 | | 13=y-13 | | 8y+3=7y-5 | | 7(6y-3)=21y | | 0=4x^3-13x^2+11x-2 | | x^2+6x-305=0 | | 7-x+5x-2-8x= | | 6x^2=-33x+18 | | .60n=45 | | 3(x+4)=-3 | | .60n=4 | | -3=9+4 | | 4(2x-3)=10 | | -3p^2-12p+36=0 | | (7x-3)(7x-3)=30 | | 30=t+5t | | 30t+5t= | | 3(x+4)=x+2(x+6) | | y+2=-4+8 | | 4(x-1)-16=0 | | 0.375x-0.3333333333x+6=0.1666666667x | | x^2+6x-16x=0 | | 3y=2(y+4) | | X+27=19 | | 0=16t^2-12t-3 | | (x+3)(x+1)=35 | | 7x-33=4x | | 3u-7u=-16+4 | | 15+4m=-1 | | 1.06x-3=0.71 | | -56x^2=-64x |

Equations solver categories