3w^2+32w+14=

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Solution for 3w^2+32w+14= equation: 


Simplifying
3w2 + 32w + 14 = 0

Reorder the terms:
14 + 32w + 3w2 = 0

Solving
14 + 32w + 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'.
4.666666667 + 10.66666667w + w2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + 10.66666667w + -4.666666667 + w2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + 10.66666667w + w2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + 10.66666667w + w2 = 0 + -4.666666667
10.66666667w + w2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
10.66666667w + w2 = -4.666666667

The w term is 10.66666667w.  Take half its coefficient (5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
10.66666667w + 28.44444446 + w2 = -4.666666667 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667w + w2 = -4.666666667 + 28.44444446

Combine like terms: -4.666666667 + 28.44444446 = 23.777777793
28.44444446 + 10.66666667w + w2 = 23.777777793

Factor a perfect square on the left side:
(w + 5.333333335)(w + 5.333333335) = 23.777777793

Calculate the square root of the right side: 4.876246281

Break this problem into two subproblems by setting 
(w + 5.333333335) equal to 4.876246281 and -4.876246281.


Subproblem 1
w + 5.333333335 = 4.876246281

Simplifying
w + 5.333333335 = 4.876246281

Reorder the terms:
5.333333335 + w = 4.876246281

Solving
5.333333335 + w = 4.876246281

Solving for variable 'w'.

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

Add '-5.333333335' to each side of the equation.
5.333333335 + -5.333333335 + w = 4.876246281 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + w = 4.876246281 + -5.333333335
w = 4.876246281 + -5.333333335

Combine like terms: 4.876246281 + -5.333333335 = -0.457087054
w = -0.457087054

Simplifying
w = -0.457087054


Subproblem 2
w + 5.333333335 = -4.876246281

Simplifying
w + 5.333333335 = -4.876246281

Reorder the terms:
5.333333335 + w = -4.876246281

Solving
5.333333335 + w = -4.876246281

Solving for variable 'w'.

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

Add '-5.333333335' to each side of the equation.
5.333333335 + -5.333333335 + w = -4.876246281 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + w = -4.876246281 + -5.333333335
w = -4.876246281 + -5.333333335

Combine like terms: -4.876246281 + -5.333333335 = -10.209579616
w = -10.209579616

Simplifying
w = -10.209579616


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.457087054, -10.209579616}

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