0.16*(w)*(w)+(1-w)*(1-w)*.0004=.3

Solution for 0.16*(w)*(w)+(1-w)*(1-w)*.0004=.3 equation:

Simplifying
0.16(w)(w) + (1 + -1w)(1 + -1w) * 0.0004 = 0.3

Multiply w * w
0.16w2 + (1 + -1w)(1 + -1w) * 0.0004 = 0.3

Reorder the terms for easier multiplication:
0.16w2 + 0.0004(1 + -1w)(1 + -1w) = 0.3

Multiply (1 + -1w) * (1 + -1w)
0.16w2 + 0.0004(1(1 + -1w) + -1w * (1 + -1w)) = 0.3
0.16w2 + 0.0004((1 * 1 + -1w * 1) + -1w * (1 + -1w)) = 0.3
0.16w2 + 0.0004((1 + -1w) + -1w * (1 + -1w)) = 0.3
0.16w2 + 0.0004(1 + -1w + (1 * -1w + -1w * -1w)) = 0.3
0.16w2 + 0.0004(1 + -1w + (-1w + 1w2)) = 0.3

Combine like terms: -1w + -1w = -2w
0.16w2 + 0.0004(1 + -2w + 1w2) = 0.3
0.16w2 + (1 * 0.0004 + -2w * 0.0004 + 1w2 * 0.0004) = 0.3
0.16w2 + (0.0004 + -0.0008w + 0.0004w2) = 0.3

Reorder the terms:
0.0004 + -0.0008w + 0.16w2 + 0.0004w2 = 0.3

Combine like terms: 0.16w2 + 0.0004w2 = 0.1604w2
0.0004 + -0.0008w + 0.1604w2 = 0.3

Solving
0.0004 + -0.0008w + 0.1604w2 = 0.3

Solving for variable 'w'.

Reorder the terms:
0.0004 + -0.3 + -0.0008w + 0.1604w2 = 0.3 + -0.3

Combine like terms: 0.0004 + -0.3 = -0.2996
-0.2996 + -0.0008w + 0.1604w2 = 0.3 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
-0.2996 + -0.0008w + 0.1604w2 = 0.0

Begin completing the square.  Divide all terms by
0.1604 the coefficient of the squared term: 

Divide each side by '0.1604'.
-1.867830424 + -0.004987531172w + w2 = 0

Move the constant term to the right:

Add '1.867830424' to each side of the equation.
-1.867830424 + -0.004987531172w + 1.867830424 + w2 = 0 + 1.867830424

Reorder the terms:
-1.867830424 + 1.867830424 + -0.004987531172w + w2 = 0 + 1.867830424

Combine like terms: -1.867830424 + 1.867830424 = 0.000000000
0.000000000 + -0.004987531172w + w2 = 0 + 1.867830424
-0.004987531172w + w2 = 0 + 1.867830424

Combine like terms: 0 + 1.867830424 = 1.867830424
-0.004987531172w + w2 = 1.867830424

The w term is -0.004987531172w.  Take half its coefficient (-0.002493765586).
Square it (0.000006218866798) and add it to both sides.

Add '0.000006218866798' to each side of the equation.
-0.004987531172w + 0.000006218866798 + w2 = 1.867830424 + 0.000006218866798

Reorder the terms:
0.000006218866798 + -0.004987531172w + w2 = 1.867830424 + 0.000006218866798

Combine like terms: 1.867830424 + 0.000006218866798 = 1.867836642866798
0.000006218866798 + -0.004987531172w + w2 = 1.867836642866798

Factor a perfect square on the left side:
(w + -0.002493765586)(w + -0.002493765586) = 1.867836642866798

Calculate the square root of the right side: 1.366688203

Break this problem into two subproblems by setting 
(w + -0.002493765586) equal to 1.366688203 and -1.366688203.

Subproblem 1
w + -0.002493765586 = 1.366688203

Simplifying
w + -0.002493765586 = 1.366688203

Reorder the terms:
-0.002493765586 + w = 1.366688203

Solving
-0.002493765586 + w = 1.366688203

Solving for variable 'w'.

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

Add '0.002493765586' to each side of the equation.
-0.002493765586 + 0.002493765586 + w = 1.366688203 + 0.002493765586

Combine like terms: -0.002493765586 + 0.002493765586 = 0.000000000000
0.000000000000 + w = 1.366688203 + 0.002493765586
w = 1.366688203 + 0.002493765586

Combine like terms: 1.366688203 + 0.002493765586 = 1.369181968586
w = 1.369181968586

Simplifying
w = 1.369181968586

Subproblem 2
w + -0.002493765586 = -1.366688203

Simplifying
w + -0.002493765586 = -1.366688203

Reorder the terms:
-0.002493765586 + w = -1.366688203

Solving
-0.002493765586 + w = -1.366688203

Solving for variable 'w'.

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

Add '0.002493765586' to each side of the equation.
-0.002493765586 + 0.002493765586 + w = -1.366688203 + 0.002493765586

Combine like terms: -0.002493765586 + 0.002493765586 = 0.000000000000
0.000000000000 + w = -1.366688203 + 0.002493765586
w = -1.366688203 + 0.002493765586

Combine like terms: -1.366688203 + 0.002493765586 = -1.364194437414
w = -1.364194437414

Simplifying
w = -1.364194437414

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.369181968586, -1.364194437414}