(3x^2-16x+18)=0

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Solution for (3x^2-16x+18)=0 equation: 


Simplifying
(3x2 + -16x + 18) = 0

Reorder the terms:
(18 + -16x + 3x2) = 0

Remove parenthesis around (18 + -16x + 3x2)
18 + -16x + 3x2 = 0

Solving
18 + -16x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
6 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -5.333333333x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -5.333333333x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5.333333333x + x2 = 0 + -6
-5.333333333x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-5.333333333x + x2 = -6

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = -6 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = -6 + 7.111111113

Combine like terms: -6 + 7.111111113 = 1.111111113
7.111111113 + -5.333333333x + x2 = 1.111111113

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 1.111111113

Calculate the square root of the right side: 1.054092554

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 1.054092554 and -1.054092554.


Subproblem 1
x + -2.666666667 = 1.054092554

Simplifying
x + -2.666666667 = 1.054092554

Reorder the terms:
-2.666666667 + x = 1.054092554

Solving
-2.666666667 + x = 1.054092554

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 1.054092554 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 1.054092554 + 2.666666667
x = 1.054092554 + 2.666666667

Combine like terms: 1.054092554 + 2.666666667 = 3.720759221
x = 3.720759221

Simplifying
x = 3.720759221


Subproblem 2
x + -2.666666667 = -1.054092554

Simplifying
x + -2.666666667 = -1.054092554

Reorder the terms:
-2.666666667 + x = -1.054092554

Solving
-2.666666667 + x = -1.054092554

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -1.054092554 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -1.054092554 + 2.666666667
x = -1.054092554 + 2.666666667

Combine like terms: -1.054092554 + 2.666666667 = 1.612574113
x = 1.612574113

Simplifying
x = 1.612574113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.720759221, 1.612574113}

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