0.4*(w)*(w)+(1-w)*(1-w)*.02=.3

Solution for 0.4*(w)*(w)+(1-w)*(1-w)*.02=.3 equation:

Simplifying
0.4(w)(w) + (1 + -1w)(1 + -1w) * 0.02 = 0.3

Multiply w * w
0.4w2 + (1 + -1w)(1 + -1w) * 0.02 = 0.3

Reorder the terms for easier multiplication:
0.4w2 + 0.02(1 + -1w)(1 + -1w) = 0.3

Multiply (1 + -1w) * (1 + -1w)
0.4w2 + 0.02(1(1 + -1w) + -1w * (1 + -1w)) = 0.3
0.4w2 + 0.02((1 * 1 + -1w * 1) + -1w * (1 + -1w)) = 0.3
0.4w2 + 0.02((1 + -1w) + -1w * (1 + -1w)) = 0.3
0.4w2 + 0.02(1 + -1w + (1 * -1w + -1w * -1w)) = 0.3
0.4w2 + 0.02(1 + -1w + (-1w + 1w2)) = 0.3

Combine like terms: -1w + -1w = -2w
0.4w2 + 0.02(1 + -2w + 1w2) = 0.3
0.4w2 + (1 * 0.02 + -2w * 0.02 + 1w2 * 0.02) = 0.3
0.4w2 + (0.02 + -0.04w + 0.02w2) = 0.3

Reorder the terms:
0.02 + -0.04w + 0.4w2 + 0.02w2 = 0.3

Combine like terms: 0.4w2 + 0.02w2 = 0.42w2
0.02 + -0.04w + 0.42w2 = 0.3

Solving
0.02 + -0.04w + 0.42w2 = 0.3

Solving for variable 'w'.

Reorder the terms:
0.02 + -0.3 + -0.04w + 0.42w2 = 0.3 + -0.3

Combine like terms: 0.02 + -0.3 = -0.28
-0.28 + -0.04w + 0.42w2 = 0.3 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
-0.28 + -0.04w + 0.42w2 = 0.0

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

Divide each side by '0.42'.
-0.6666666667 + -0.09523809524w + w2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -0.09523809524w + 0.6666666667 + w2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -0.09523809524w + w2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -0.09523809524w + w2 = 0 + 0.6666666667
-0.09523809524w + w2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-0.09523809524w + w2 = 0.6666666667

The w term is -0.09523809524w.  Take half its coefficient (-0.04761904762).
Square it (0.002267573696) and add it to both sides.

Add '0.002267573696' to each side of the equation.
-0.09523809524w + 0.002267573696 + w2 = 0.6666666667 + 0.002267573696

Reorder the terms:
0.002267573696 + -0.09523809524w + w2 = 0.6666666667 + 0.002267573696

Combine like terms: 0.6666666667 + 0.002267573696 = 0.668934240396
0.002267573696 + -0.09523809524w + w2 = 0.668934240396

Factor a perfect square on the left side:
(w + -0.04761904762)(w + -0.04761904762) = 0.668934240396

Calculate the square root of the right side: 0.817884002

Break this problem into two subproblems by setting 
(w + -0.04761904762) equal to 0.817884002 and -0.817884002.

Subproblem 1
w + -0.04761904762 = 0.817884002

Simplifying
w + -0.04761904762 = 0.817884002

Reorder the terms:
-0.04761904762 + w = 0.817884002

Solving
-0.04761904762 + w = 0.817884002

Solving for variable 'w'.

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

Add '0.04761904762' to each side of the equation.
-0.04761904762 + 0.04761904762 + w = 0.817884002 + 0.04761904762

Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000
0.00000000000 + w = 0.817884002 + 0.04761904762
w = 0.817884002 + 0.04761904762

Combine like terms: 0.817884002 + 0.04761904762 = 0.86550304962
w = 0.86550304962

Simplifying
w = 0.86550304962

Subproblem 2
w + -0.04761904762 = -0.817884002

Simplifying
w + -0.04761904762 = -0.817884002

Reorder the terms:
-0.04761904762 + w = -0.817884002

Solving
-0.04761904762 + w = -0.817884002

Solving for variable 'w'.

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

Add '0.04761904762' to each side of the equation.
-0.04761904762 + 0.04761904762 + w = -0.817884002 + 0.04761904762

Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000
0.00000000000 + w = -0.817884002 + 0.04761904762
w = -0.817884002 + 0.04761904762

Combine like terms: -0.817884002 + 0.04761904762 = -0.77026495438
w = -0.77026495438

Simplifying
w = -0.77026495438

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.86550304962, -0.77026495438}