3x^2-18x+7=0

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Solution for 3x^2-18x+7=0 equation: 


Simplifying
3x2 + -18x + 7 = 0

Reorder the terms:
7 + -18x + 3x2 = 0

Solving
7 + -18x + 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'.
2.333333333 + -6x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -6x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -6x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -6x + x2 = 0 + -2.333333333
-6x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-6x + x2 = -2.333333333

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -2.333333333 + 9

Reorder the terms:
9 + -6x + x2 = -2.333333333 + 9

Combine like terms: -2.333333333 + 9 = 6.666666667
9 + -6x + x2 = 6.666666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 6.666666667

Calculate the square root of the right side: 2.581988898

Break this problem into two subproblems by setting 
(x + -3) equal to 2.581988898 and -2.581988898.


Subproblem 1
x + -3 = 2.581988898

Simplifying
x + -3 = 2.581988898

Reorder the terms:
-3 + x = 2.581988898

Solving
-3 + x = 2.581988898

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.581988898 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.581988898 + 3
x = 2.581988898 + 3

Combine like terms: 2.581988898 + 3 = 5.581988898
x = 5.581988898

Simplifying
x = 5.581988898


Subproblem 2
x + -3 = -2.581988898

Simplifying
x + -3 = -2.581988898

Reorder the terms:
-3 + x = -2.581988898

Solving
-3 + x = -2.581988898

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.581988898 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.581988898 + 3
x = -2.581988898 + 3

Combine like terms: -2.581988898 + 3 = 0.418011102
x = 0.418011102

Simplifying
x = 0.418011102


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.581988898, 0.418011102}

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