160=(2W-2)W

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Solution for 160=(2W-2)W equation: 


Simplifying
160 = (2W + -2) * W

Reorder the terms:
160 = (-2 + 2W) * W

Reorder the terms for easier multiplication:
160 = W(-2 + 2W)
160 = (-2 * W + 2W * W)
160 = (-2W + 2W2)

Solving
160 = -2W + 2W2

Solving for variable 'W'.

Reorder the terms:
160 + 2W + -2W2 = -2W + 2W + 2W2 + -2W2

Combine like terms: -2W + 2W = 0
160 + 2W + -2W2 = 0 + 2W2 + -2W2
160 + 2W + -2W2 = 2W2 + -2W2

Combine like terms: 2W2 + -2W2 = 0
160 + 2W + -2W2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(80 + W + -1W2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(80 + W + -1W2)' equal to zero and attempt to solve:

Simplifying
80 + W + -1W2 = 0

Solving
80 + W + -1W2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-80 + -1W + W2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -1W + 80 + W2 = 0 + 80

Reorder the terms:
-80 + 80 + -1W + W2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -1W + W2 = 0 + 80
-1W + W2 = 0 + 80

Combine like terms: 0 + 80 = 80
-1W + W2 = 80

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.
-1W + 0.25 + W2 = 80 + 0.25

Reorder the terms:
0.25 + -1W + W2 = 80 + 0.25

Combine like terms: 80 + 0.25 = 80.25
0.25 + -1W + W2 = 80.25

Factor a perfect square on the left side:
(W + 0.5)(W + 0.5) = 80.25

Calculate the square root of the right side: 8.958236434

Break this problem into two subproblems by setting 
(W + 0.5) equal to 8.958236434 and -8.958236434.


Subproblem 1
W + 0.5 = 8.958236434

Simplifying
W + 0.5 = 8.958236434

Reorder the terms:
0.5 + W = 8.958236434

Solving
0.5 + W = 8.958236434

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 = 8.958236434 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + W = 8.958236434 + -0.5
W = 8.958236434 + -0.5

Combine like terms: 8.958236434 + -0.5 = 8.458236434
W = 8.458236434

Simplifying
W = 8.458236434


Subproblem 2
W + 0.5 = -8.958236434

Simplifying
W + 0.5 = -8.958236434

Reorder the terms:
0.5 + W = -8.958236434

Solving
0.5 + W = -8.958236434

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 = -8.958236434 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + W = -8.958236434 + -0.5
W = -8.958236434 + -0.5

Combine like terms: -8.958236434 + -0.5 = -9.458236434
W = -9.458236434

Simplifying
W = -9.458236434


Solution
The solution to the problem is based on the solutions
from the subproblems.
W = {8.458236434, -9.458236434}
Solution
W = {8.458236434, -9.458236434}

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