3w^2-22w-6=0

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Solution for 3w^2-22w-6=0 equation: 


Simplifying
3w2 + -22w + -6 = 0

Reorder the terms:
-6 + -22w + 3w2 = 0

Solving
-6 + -22w + 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 + -7.333333333w + w2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -7.333333333w + 2 + w2 = 0 + 2

Reorder the terms:
-2 + 2 + -7.333333333w + w2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7.333333333w + w2 = 0 + 2
-7.333333333w + w2 = 0 + 2

Combine like terms: 0 + 2 = 2
-7.333333333w + w2 = 2

The w term is -7.333333333w.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333w + 13.44444445 + w2 = 2 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333w + w2 = 2 + 13.44444445

Combine like terms: 2 + 13.44444445 = 15.44444445
13.44444445 + -7.333333333w + w2 = 15.44444445

Factor a perfect square on the left side:
(w + -3.666666667)(w + -3.666666667) = 15.44444445

Calculate the square root of the right side: 3.929942042

Break this problem into two subproblems by setting 
(w + -3.666666667) equal to 3.929942042 and -3.929942042.


Subproblem 1
w + -3.666666667 = 3.929942042

Simplifying
w + -3.666666667 = 3.929942042

Reorder the terms:
-3.666666667 + w = 3.929942042

Solving
-3.666666667 + w = 3.929942042

Solving for variable 'w'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + w = 3.929942042 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + w = 3.929942042 + 3.666666667
w = 3.929942042 + 3.666666667

Combine like terms: 3.929942042 + 3.666666667 = 7.596608709
w = 7.596608709

Simplifying
w = 7.596608709


Subproblem 2
w + -3.666666667 = -3.929942042

Simplifying
w + -3.666666667 = -3.929942042

Reorder the terms:
-3.666666667 + w = -3.929942042

Solving
-3.666666667 + w = -3.929942042

Solving for variable 'w'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + w = -3.929942042 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + w = -3.929942042 + 3.666666667
w = -3.929942042 + 3.666666667

Combine like terms: -3.929942042 + 3.666666667 = -0.263275375
w = -0.263275375

Simplifying
w = -0.263275375


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.596608709, -0.263275375}

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