3w^2-8w-4=0

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Solution for 3w^2-8w-4=0 equation: 


Simplifying
3w2 + -8w + -4 = 0

Reorder the terms:
-4 + -8w + 3w2 = 0

Solving
-4 + -8w + 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'.
-1.333333333 + -2.666666667w + w2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -2.666666667w + 1.333333333 + w2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -2.666666667w + w2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -2.666666667w + w2 = 0 + 1.333333333
-2.666666667w + w2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-2.666666667w + w2 = 1.333333333

The w term is -2.666666667w.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667w + 1.777777780 + w2 = 1.333333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667w + w2 = 1.333333333 + 1.777777780

Combine like terms: 1.333333333 + 1.777777780 = 3.111111113
1.777777780 + -2.666666667w + w2 = 3.111111113

Factor a perfect square on the left side:
(w + -1.333333334)(w + -1.333333334) = 3.111111113

Calculate the square root of the right side: 1.763834208

Break this problem into two subproblems by setting 
(w + -1.333333334) equal to 1.763834208 and -1.763834208.


Subproblem 1
w + -1.333333334 = 1.763834208

Simplifying
w + -1.333333334 = 1.763834208

Reorder the terms:
-1.333333334 + w = 1.763834208

Solving
-1.333333334 + w = 1.763834208

Solving for variable 'w'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + w = 1.763834208 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + w = 1.763834208 + 1.333333334
w = 1.763834208 + 1.333333334

Combine like terms: 1.763834208 + 1.333333334 = 3.097167542
w = 3.097167542

Simplifying
w = 3.097167542


Subproblem 2
w + -1.333333334 = -1.763834208

Simplifying
w + -1.333333334 = -1.763834208

Reorder the terms:
-1.333333334 + w = -1.763834208

Solving
-1.333333334 + w = -1.763834208

Solving for variable 'w'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + w = -1.763834208 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + w = -1.763834208 + 1.333333334
w = -1.763834208 + 1.333333334

Combine like terms: -1.763834208 + 1.333333334 = -0.430500874
w = -0.430500874

Simplifying
w = -0.430500874


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.097167542, -0.430500874}

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