6w^2-w-28=0

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Solution for 6w^2-w-28=0 equation: 


Simplifying
6w2 + -1w + -28 = 0

Reorder the terms:
-28 + -1w + 6w2 = 0

Solving
-28 + -1w + 6w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-4.666666667 + -0.1666666667w + w2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -0.1666666667w + 4.666666667 + w2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -0.1666666667w + w2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -0.1666666667w + w2 = 0 + 4.666666667
-0.1666666667w + w2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-0.1666666667w + w2 = 4.666666667

The w term is -0.1666666667w.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667w + 0.006944444447 + w2 = 4.666666667 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667w + w2 = 4.666666667 + 0.006944444447

Combine like terms: 4.666666667 + 0.006944444447 = 4.673611111447
0.006944444447 + -0.1666666667w + w2 = 4.673611111447

Factor a perfect square on the left side:
(w + -0.08333333335)(w + -0.08333333335) = 4.673611111447

Calculate the square root of the right side: 2.161853629

Break this problem into two subproblems by setting 
(w + -0.08333333335) equal to 2.161853629 and -2.161853629.


Subproblem 1
w + -0.08333333335 = 2.161853629

Simplifying
w + -0.08333333335 = 2.161853629

Reorder the terms:
-0.08333333335 + w = 2.161853629

Solving
-0.08333333335 + w = 2.161853629

Solving for variable 'w'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + w = 2.161853629 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + w = 2.161853629 + 0.08333333335
w = 2.161853629 + 0.08333333335

Combine like terms: 2.161853629 + 0.08333333335 = 2.24518696235
w = 2.24518696235

Simplifying
w = 2.24518696235


Subproblem 2
w + -0.08333333335 = -2.161853629

Simplifying
w + -0.08333333335 = -2.161853629

Reorder the terms:
-0.08333333335 + w = -2.161853629

Solving
-0.08333333335 + w = -2.161853629

Solving for variable 'w'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + w = -2.161853629 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + w = -2.161853629 + 0.08333333335
w = -2.161853629 + 0.08333333335

Combine like terms: -2.161853629 + 0.08333333335 = -2.07852029565
w = -2.07852029565

Simplifying
w = -2.07852029565


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.24518696235, -2.07852029565}

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