3w^2-18w+1=0

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Solution for 3w^2-18w+1=0 equation: 


Simplifying
3w2 + -18w + 1 = 0

Reorder the terms:
1 + -18w + 3w2 = 0

Solving
1 + -18w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
0.3333333333 + -6w + w2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -6w + -0.3333333333 + w2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -6w + w2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -6w + w2 = 0 + -0.3333333333
-6w + w2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-6w + w2 = -0.3333333333

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

Add '9' to each side of the equation.
-6w + 9 + w2 = -0.3333333333 + 9

Reorder the terms:
9 + -6w + w2 = -0.3333333333 + 9

Combine like terms: -0.3333333333 + 9 = 8.6666666667
9 + -6w + w2 = 8.6666666667

Factor a perfect square on the left side:
(w + -3)(w + -3) = 8.6666666667

Calculate the square root of the right side: 2.943920289

Break this problem into two subproblems by setting 
(w + -3) equal to 2.943920289 and -2.943920289.


Subproblem 1
w + -3 = 2.943920289

Simplifying
w + -3 = 2.943920289

Reorder the terms:
-3 + w = 2.943920289

Solving
-3 + w = 2.943920289

Solving for variable 'w'.

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

Add '3' to each side of the equation.
-3 + 3 + w = 2.943920289 + 3

Combine like terms: -3 + 3 = 0
0 + w = 2.943920289 + 3
w = 2.943920289 + 3

Combine like terms: 2.943920289 + 3 = 5.943920289
w = 5.943920289

Simplifying
w = 5.943920289


Subproblem 2
w + -3 = -2.943920289

Simplifying
w + -3 = -2.943920289

Reorder the terms:
-3 + w = -2.943920289

Solving
-3 + w = -2.943920289

Solving for variable 'w'.

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

Add '3' to each side of the equation.
-3 + 3 + w = -2.943920289 + 3

Combine like terms: -3 + 3 = 0
0 + w = -2.943920289 + 3
w = -2.943920289 + 3

Combine like terms: -2.943920289 + 3 = 0.056079711
w = 0.056079711

Simplifying
w = 0.056079711


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.943920289, 0.056079711}

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