3w^2+145w+8=0

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Solution for 3w^2+145w+8=0 equation: 


Simplifying
3w2 + 145w + 8 = 0

Reorder the terms:
8 + 145w + 3w2 = 0

Solving
8 + 145w + 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'.
2.666666667 + 48.33333333w + w2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 48.33333333w + -2.666666667 + w2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 48.33333333w + w2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 48.33333333w + w2 = 0 + -2.666666667
48.33333333w + w2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
48.33333333w + w2 = -2.666666667

The w term is 48.33333333w.  Take half its coefficient (24.16666667).
Square it (584.0277779) and add it to both sides.

Add '584.0277779' to each side of the equation.
48.33333333w + 584.0277779 + w2 = -2.666666667 + 584.0277779

Reorder the terms:
584.0277779 + 48.33333333w + w2 = -2.666666667 + 584.0277779

Combine like terms: -2.666666667 + 584.0277779 = 581.361111233
584.0277779 + 48.33333333w + w2 = 581.361111233

Factor a perfect square on the left side:
(w + 24.16666667)(w + 24.16666667) = 581.361111233

Calculate the square root of the right side: 24.111431132

Break this problem into two subproblems by setting 
(w + 24.16666667) equal to 24.111431132 and -24.111431132.


Subproblem 1
w + 24.16666667 = 24.111431132

Simplifying
w + 24.16666667 = 24.111431132

Reorder the terms:
24.16666667 + w = 24.111431132

Solving
24.16666667 + w = 24.111431132

Solving for variable 'w'.

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

Add '-24.16666667' to each side of the equation.
24.16666667 + -24.16666667 + w = 24.111431132 + -24.16666667

Combine like terms: 24.16666667 + -24.16666667 = 0.00000000
0.00000000 + w = 24.111431132 + -24.16666667
w = 24.111431132 + -24.16666667

Combine like terms: 24.111431132 + -24.16666667 = -0.055235538
w = -0.055235538

Simplifying
w = -0.055235538


Subproblem 2
w + 24.16666667 = -24.111431132

Simplifying
w + 24.16666667 = -24.111431132

Reorder the terms:
24.16666667 + w = -24.111431132

Solving
24.16666667 + w = -24.111431132

Solving for variable 'w'.

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

Add '-24.16666667' to each side of the equation.
24.16666667 + -24.16666667 + w = -24.111431132 + -24.16666667

Combine like terms: 24.16666667 + -24.16666667 = 0.00000000
0.00000000 + w = -24.111431132 + -24.16666667
w = -24.111431132 + -24.16666667

Combine like terms: -24.111431132 + -24.16666667 = -48.278097802
w = -48.278097802

Simplifying
w = -48.278097802


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.055235538, -48.278097802}

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