3w^2-11w-8=0

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Solution for 3w^2-11w-8=0 equation: 


Simplifying
3w2 + -11w + -8 = 0

Reorder the terms:
-8 + -11w + 3w2 = 0

Solving
-8 + -11w + 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 + -3.666666667w + w2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -3.666666667w + 2.666666667 + w2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -3.666666667w + w2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -3.666666667w + w2 = 0 + 2.666666667
-3.666666667w + w2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-3.666666667w + w2 = 2.666666667

The w term is -3.666666667w.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667w + 3.361111114 + w2 = 2.666666667 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667w + w2 = 2.666666667 + 3.361111114

Combine like terms: 2.666666667 + 3.361111114 = 6.027777781
3.361111114 + -3.666666667w + w2 = 6.027777781

Factor a perfect square on the left side:
(w + -1.833333334)(w + -1.833333334) = 6.027777781

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(w + -1.833333334) equal to 2.455153311 and -2.455153311.


Subproblem 1
w + -1.833333334 = 2.455153311

Simplifying
w + -1.833333334 = 2.455153311

Reorder the terms:
-1.833333334 + w = 2.455153311

Solving
-1.833333334 + w = 2.455153311

Solving for variable 'w'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + w = 2.455153311 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + w = 2.455153311 + 1.833333334
w = 2.455153311 + 1.833333334

Combine like terms: 2.455153311 + 1.833333334 = 4.288486645
w = 4.288486645

Simplifying
w = 4.288486645


Subproblem 2
w + -1.833333334 = -2.455153311

Simplifying
w + -1.833333334 = -2.455153311

Reorder the terms:
-1.833333334 + w = -2.455153311

Solving
-1.833333334 + w = -2.455153311

Solving for variable 'w'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + w = -2.455153311 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + w = -2.455153311 + 1.833333334
w = -2.455153311 + 1.833333334

Combine like terms: -2.455153311 + 1.833333334 = -0.621819977
w = -0.621819977

Simplifying
w = -0.621819977


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.288486645, -0.621819977}

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