16=2w(2w+w-1)

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Solution for 16=2w(2w+w-1) equation: 


Simplifying
16 = 2w(2w + w + -1)

Reorder the terms:
16 = 2w(-1 + 2w + w)

Combine like terms: 2w + w = 3w
16 = 2w(-1 + 3w)
16 = (-1 * 2w + 3w * 2w)
16 = (-2w + 6w2)

Solving
16 = -2w + 6w2

Solving for variable 'w'.

Reorder the terms:
16 + 2w + -6w2 = -2w + 2w + 6w2 + -6w2

Combine like terms: -2w + 2w = 0
16 + 2w + -6w2 = 0 + 6w2 + -6w2
16 + 2w + -6w2 = 6w2 + -6w2

Combine like terms: 6w2 + -6w2 = 0
16 + 2w + -6w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + w + -3w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + w + -3w2)' equal to zero and attempt to solve:

Simplifying
8 + w + -3w2 = 0

Solving
8 + w + -3w2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2.666666667 + -0.3333333333w + w2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -0.3333333333w + 2.666666667 + w2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -0.3333333333w + w2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -0.3333333333w + w2 = 0 + 2.666666667
-0.3333333333w + w2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-0.3333333333w + w2 = 2.666666667

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.3333333333w + 0.25 + w2 = 2.666666667 + 0.25

Reorder the terms:
0.25 + -0.3333333333w + w2 = 2.666666667 + 0.25

Combine like terms: 2.666666667 + 0.25 = 2.916666667
0.25 + -0.3333333333w + w2 = 2.916666667

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(w + 0.5) equal to 1.707825128 and -1.707825128.


Subproblem 1
w + 0.5 = 1.707825128

Simplifying
w + 0.5 = 1.707825128

Reorder the terms:
0.5 + w = 1.707825128

Solving
0.5 + w = 1.707825128

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 1.707825128 + -0.5
w = 1.707825128 + -0.5

Combine like terms: 1.707825128 + -0.5 = 1.207825128
w = 1.207825128

Simplifying
w = 1.207825128


Subproblem 2
w + 0.5 = -1.707825128

Simplifying
w + 0.5 = -1.707825128

Reorder the terms:
0.5 + w = -1.707825128

Solving
0.5 + w = -1.707825128

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -1.707825128 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -1.707825128 + -0.5
w = -1.707825128 + -0.5

Combine like terms: -1.707825128 + -0.5 = -2.207825128
w = -2.207825128

Simplifying
w = -2.207825128


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.207825128, -2.207825128}
Solution
w = {1.207825128, -2.207825128}

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