6x^2-18x+4=0

Simple and best practice solution for 6x^2-18x+4=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^2-18x+4=0 equation: 


Simplifying
6x2 + -18x + 4 = 0

Reorder the terms:
4 + -18x + 6x2 = 0

Solving
4 + -18x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -9x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -9x + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + -9x + 3x2 = 0

Solving
2 + -9x + 3x2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -3x + x2 = 0 + -0.6666666667
-3x + x2 = 0 + -0.6666666667

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

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -0.6666666667 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.6666666667 + 2.25

Combine like terms: -0.6666666667 + 2.25 = 1.5833333333
2.25 + -3x + x2 = 1.5833333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.5833333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.258305739 and -1.258305739.


Subproblem 1
x + -1.5 = 1.258305739

Simplifying
x + -1.5 = 1.258305739

Reorder the terms:
-1.5 + x = 1.258305739

Solving
-1.5 + x = 1.258305739

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.258305739 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.258305739 + 1.5
x = 1.258305739 + 1.5

Combine like terms: 1.258305739 + 1.5 = 2.758305739
x = 2.758305739

Simplifying
x = 2.758305739


Subproblem 2
x + -1.5 = -1.258305739

Simplifying
x + -1.5 = -1.258305739

Reorder the terms:
-1.5 + x = -1.258305739

Solving
-1.5 + x = -1.258305739

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.258305739 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.258305739 + 1.5
x = -1.258305739 + 1.5

Combine like terms: -1.258305739 + 1.5 = 0.241694261
x = 0.241694261

Simplifying
x = 0.241694261


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.758305739, 0.241694261}
Solution
x = {2.758305739, 0.241694261}

See similar equations:

| -2y-3g+8=8-5y-12 | | 14=1b-1 | | n/10=-3 | | a/2=-20 | | 5000-2945= | | r/3=13 | | 15=-4d+3d | | k/13=11 | | .8333+g=4.67 | | -16=-7(5h-9) | | x/20=-13 | | x^2-kx-c=0 | | y=35x+25 | | 4x^2+66x-280= | | y=-8z^2 | | 5(f+5)-4(f-3)= | | m/8=120 | | 7(x+3)+5=5(x-6)+x-4+x | | m^2=-3m+40 | | 2[0]+4[y]=16 | | 6(4y+7)=-29 | | 6x^2=-51.75 | | -0.3(-0.6-2x)=1.1x | | x-3/5x=8 | | 5u^2-9u+4=0 | | 2[2]+4[y]=16 | | 1/1-10i | | 2[-2]+4[y]=16 | | 3a-6a+12=30 | | 90=4x+6 | | X(7x+8)=2x^2-21x+42 | | 3-2m=-(3m-5) |

Equations solver categories