0.05=W^2*0.06+(1-W^2)*0.11+2(0.1)*W(1-W)*0.245*0.332

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Solution for 0.05=W^2*0.06+(1-W^2)*0.11+2(0.1)*W(1-W)*0.245*0.332 equation: 


Simplifying
0.05 = W2 * 0.06 + (1 + -1W2) * 0.11 + 2(0.1) * W(1 + -1W) * 0.245 * 0.332

Reorder the terms for easier multiplication:
0.05 = 0.06W2 + (1 + -1W2) * 0.11 + 2(0.1) * W(1 + -1W) * 0.245 * 0.332

Reorder the terms for easier multiplication:
0.05 = 0.06W2 + 0.11(1 + -1W2) + 2(0.1) * W(1 + -1W) * 0.245 * 0.332
0.05 = 0.06W2 + (1 * 0.11 + -1W2 * 0.11) + 2(0.1) * W(1 + -1W) * 0.245 * 0.332
0.05 = 0.06W2 + (0.11 + -0.11W2) + 2(0.1) * W(1 + -1W) * 0.245 * 0.332

Reorder the terms for easier multiplication:
0.05 = 0.06W2 + 0.11 + -0.11W2 + 2 * 0.1 * 0.245 * 0.332W(1 + -1W)

Multiply 2 * 0.1
0.05 = 0.06W2 + 0.11 + -0.11W2 + 0.2 * 0.245 * 0.332W(1 + -1W)

Multiply 0.2 * 0.245
0.05 = 0.06W2 + 0.11 + -0.11W2 + 0.049 * 0.332W(1 + -1W)

Multiply 0.049 * 0.332
0.05 = 0.06W2 + 0.11 + -0.11W2 + 0.016268W(1 + -1W)
0.05 = 0.06W2 + 0.11 + -0.11W2 + (1 * 0.016268W + -1W * 0.016268W)
0.05 = 0.06W2 + 0.11 + -0.11W2 + (0.016268W + -0.016268W2)

Reorder the terms:
0.05 = 0.11 + 0.016268W + 0.06W2 + -0.11W2 + -0.016268W2

Combine like terms: 0.06W2 + -0.11W2 = -0.05W2
0.05 = 0.11 + 0.016268W + -0.05W2 + -0.016268W2

Combine like terms: -0.05W2 + -0.016268W2 = -0.066268W2
0.05 = 0.11 + 0.016268W + -0.066268W2

Solving
0.05 = 0.11 + 0.016268W + -0.066268W2

Solving for variable 'W'.

Combine like terms: 0.05 + -0.11 = -0.06
-0.06 + -0.016268W + 0.066268W2 = 0.11 + 0.016268W + -0.066268W2 + -0.11 + -0.016268W + 0.066268W2

Reorder the terms:
-0.06 + -0.016268W + 0.066268W2 = 0.11 + -0.11 + 0.016268W + -0.016268W + -0.066268W2 + 0.066268W2

Combine like terms: 0.11 + -0.11 = 0.00
-0.06 + -0.016268W + 0.066268W2 = 0.00 + 0.016268W + -0.016268W + -0.066268W2 + 0.066268W2
-0.06 + -0.016268W + 0.066268W2 = 0.016268W + -0.016268W + -0.066268W2 + 0.066268W2

Combine like terms: 0.016268W + -0.016268W = 0.000000
-0.06 + -0.016268W + 0.066268W2 = 0.000000 + -0.066268W2 + 0.066268W2
-0.06 + -0.016268W + 0.066268W2 = -0.066268W2 + 0.066268W2

Combine like terms: -0.066268W2 + 0.066268W2 = 0.000000
-0.06 + -0.016268W + 0.066268W2 = 0.000000

Begin completing the square.  Divide all terms by
0.066268 the coefficient of the squared term: 

Divide each side by '0.066268'.
-0.905414378 + -0.2454880183W + W2 = 0

Move the constant term to the right:

Add '0.905414378' to each side of the equation.
-0.905414378 + -0.2454880183W + 0.905414378 + W2 = 0 + 0.905414378

Reorder the terms:
-0.905414378 + 0.905414378 + -0.2454880183W + W2 = 0 + 0.905414378

Combine like terms: -0.905414378 + 0.905414378 = 0.000000000
0.000000000 + -0.2454880183W + W2 = 0 + 0.905414378
-0.2454880183W + W2 = 0 + 0.905414378

Combine like terms: 0 + 0.905414378 = 0.905414378
-0.2454880183W + W2 = 0.905414378

The W term is -0.2454880183W.  Take half its coefficient (-0.1227440092).
Square it (0.01506609179) and add it to both sides.

Add '0.01506609179' to each side of the equation.
-0.2454880183W + 0.01506609179 + W2 = 0.905414378 + 0.01506609179

Reorder the terms:
0.01506609179 + -0.2454880183W + W2 = 0.905414378 + 0.01506609179

Combine like terms: 0.905414378 + 0.01506609179 = 0.92048046979
0.01506609179 + -0.2454880183W + W2 = 0.92048046979

Factor a perfect square on the left side:
(W + -0.1227440092)(W + -0.1227440092) = 0.92048046979

Calculate the square root of the right side: 0.959416734

Break this problem into two subproblems by setting 
(W + -0.1227440092) equal to 0.959416734 and -0.959416734.


Subproblem 1
W + -0.1227440092 = 0.959416734

Simplifying
W + -0.1227440092 = 0.959416734

Reorder the terms:
-0.1227440092 + W = 0.959416734

Solving
-0.1227440092 + W = 0.959416734

Solving for variable 'W'.

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

Add '0.1227440092' to each side of the equation.
-0.1227440092 + 0.1227440092 + W = 0.959416734 + 0.1227440092

Combine like terms: -0.1227440092 + 0.1227440092 = 0.0000000000
0.0000000000 + W = 0.959416734 + 0.1227440092
W = 0.959416734 + 0.1227440092

Combine like terms: 0.959416734 + 0.1227440092 = 1.0821607432
W = 1.0821607432

Simplifying
W = 1.0821607432


Subproblem 2
W + -0.1227440092 = -0.959416734

Simplifying
W + -0.1227440092 = -0.959416734

Reorder the terms:
-0.1227440092 + W = -0.959416734

Solving
-0.1227440092 + W = -0.959416734

Solving for variable 'W'.

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

Add '0.1227440092' to each side of the equation.
-0.1227440092 + 0.1227440092 + W = -0.959416734 + 0.1227440092

Combine like terms: -0.1227440092 + 0.1227440092 = 0.0000000000
0.0000000000 + W = -0.959416734 + 0.1227440092
W = -0.959416734 + 0.1227440092

Combine like terms: -0.959416734 + 0.1227440092 = -0.8366727248
W = -0.8366727248

Simplifying
W = -0.8366727248


Solution
The solution to the problem is based on the solutions
from the subproblems.
W = {1.0821607432, -0.8366727248}

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