6x^2+33x-54=0

Simple and best practice solution for 6x^2+33x-54=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-54=0 equation: 


Simplifying
6x2 + 33x + -54 = 0

Reorder the terms:
-54 + 33x + 6x2 = 0

Solving
-54 + 33x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + 11x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-18 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
-18 + 11x + 2x2 = 0

Solving
-18 + 11x + 2x2 = 0

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

Divide each side by '2'.
-9 + 5.5x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 5.5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 5.5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 5.5x + x2 = 0 + 9
5.5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
5.5x + x2 = 9

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 = 9 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 9 + 7.5625

Combine like terms: 9 + 7.5625 = 16.5625
7.5625 + 5.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + 2.75) equal to 4.069705149 and -4.069705149.


Subproblem 1
x + 2.75 = 4.069705149

Simplifying
x + 2.75 = 4.069705149

Reorder the terms:
2.75 + x = 4.069705149

Solving
2.75 + x = 4.069705149

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 = 4.069705149 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 4.069705149 + -2.75
x = 4.069705149 + -2.75

Combine like terms: 4.069705149 + -2.75 = 1.319705149
x = 1.319705149

Simplifying
x = 1.319705149


Subproblem 2
x + 2.75 = -4.069705149

Simplifying
x + 2.75 = -4.069705149

Reorder the terms:
2.75 + x = -4.069705149

Solving
2.75 + x = -4.069705149

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 = -4.069705149 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -4.069705149 + -2.75
x = -4.069705149 + -2.75

Combine like terms: -4.069705149 + -2.75 = -6.819705149
x = -6.819705149

Simplifying
x = -6.819705149


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.319705149, -6.819705149}
Solution
x = {1.319705149, -6.819705149}

See similar equations:

| (6)(5)(2/3) | | y^3-13y^2=-42y | | (5/3)(3/2)(4/5) | | 6-8k=-9k | | 12x-7=3x+20 | | 3z=1/5 | | 26t+21=34 | | 7m+1=-7+9m | | 7m+1=-7+9 | | (X-y^2x)dx+(y-x^2y)dy=0 | | 2d^2+5d+12=0 | | N+2n+n-5=15 | | 3h+7h-10=9h-3 | | y=90-40 | | (4x+7)=35 | | 6.2-x=4.2 | | 1/1౦y=1/7 | | -(n-7)-n=8(6+n)+6 | | (ln)x^2=7 | | -8-3p=8-7p | | 1/10y=1/7 | | Y=8x-x+26 | | 7+2d=19 | | 1+2x=71 | | (73-z)4=80 | | -12t=11 | | -13=2+3w | | 4x^2-60x-144=0 | | ×/3=15 | | -10-d=d+10 | | 4p-14=6 | | 12x+13+y=180 |

Equations solver categories