3w^2-17w+1=0

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Solution for 3w^2-17w+1=0 equation: 


Simplifying
3w2 + -17w + 1 = 0

Reorder the terms:
1 + -17w + 3w2 = 0

Solving
1 + -17w + 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 + -5.666666667w + w2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -5.666666667w + -0.3333333333 + w2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -5.666666667w + w2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -5.666666667w + w2 = 0 + -0.3333333333
-5.666666667w + w2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-5.666666667w + w2 = -0.3333333333

The w term is -5.666666667w.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667w + 8.027777782 + w2 = -0.3333333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667w + w2 = -0.3333333333 + 8.027777782

Combine like terms: -0.3333333333 + 8.027777782 = 7.6944444487
8.027777782 + -5.666666667w + w2 = 7.6944444487

Factor a perfect square on the left side:
(w + -2.833333334)(w + -2.833333334) = 7.6944444487

Calculate the square root of the right side: 2.773886164

Break this problem into two subproblems by setting 
(w + -2.833333334) equal to 2.773886164 and -2.773886164.


Subproblem 1
w + -2.833333334 = 2.773886164

Simplifying
w + -2.833333334 = 2.773886164

Reorder the terms:
-2.833333334 + w = 2.773886164

Solving
-2.833333334 + w = 2.773886164

Solving for variable 'w'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + w = 2.773886164 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + w = 2.773886164 + 2.833333334
w = 2.773886164 + 2.833333334

Combine like terms: 2.773886164 + 2.833333334 = 5.607219498
w = 5.607219498

Simplifying
w = 5.607219498


Subproblem 2
w + -2.833333334 = -2.773886164

Simplifying
w + -2.833333334 = -2.773886164

Reorder the terms:
-2.833333334 + w = -2.773886164

Solving
-2.833333334 + w = -2.773886164

Solving for variable 'w'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + w = -2.773886164 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + w = -2.773886164 + 2.833333334
w = -2.773886164 + 2.833333334

Combine like terms: -2.773886164 + 2.833333334 = 0.05944717
w = 0.05944717

Simplifying
w = 0.05944717


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.607219498, 0.05944717}

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