0.042=w(1-0.59w)

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Solution for 0.042=w(1-0.59w) equation:


Simplifying
0.042 = w(1 + -0.59w)
0.042 = (1 * w + -0.59w * w)
0.042 = (1w + -0.59w2)

Solving
0.042 = 1w + -0.59w2

Solving for variable 'w'.

Reorder the terms:
0.042 + -1w + 0.59w2 = 1w + -1w + -0.59w2 + 0.59w2

Combine like terms: 1w + -1w = 0
0.042 + -1w + 0.59w2 = 0 + -0.59w2 + 0.59w2
0.042 + -1w + 0.59w2 = -0.59w2 + 0.59w2

Combine like terms: -0.59w2 + 0.59w2 = 0.00
0.042 + -1w + 0.59w2 = 0.00

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

Divide each side by '0.59'.
0.07118644068 + -1.694915254w + w2 = 0

Move the constant term to the right:

Add '-0.07118644068' to each side of the equation.
0.07118644068 + -1.694915254w + -0.07118644068 + w2 = 0 + -0.07118644068

Reorder the terms:
0.07118644068 + -0.07118644068 + -1.694915254w + w2 = 0 + -0.07118644068

Combine like terms: 0.07118644068 + -0.07118644068 = 0.00000000000
0.00000000000 + -1.694915254w + w2 = 0 + -0.07118644068
-1.694915254w + w2 = 0 + -0.07118644068

Combine like terms: 0 + -0.07118644068 = -0.07118644068
-1.694915254w + w2 = -0.07118644068

The w term is -1.694915254w.  Take half its coefficient (-0.847457627).
Square it (0.7181844296) and add it to both sides.

Add '0.7181844296' to each side of the equation.
-1.694915254w + 0.7181844296 + w2 = -0.07118644068 + 0.7181844296

Reorder the terms:
0.7181844296 + -1.694915254w + w2 = -0.07118644068 + 0.7181844296

Combine like terms: -0.07118644068 + 0.7181844296 = 0.64699798892
0.7181844296 + -1.694915254w + w2 = 0.64699798892

Factor a perfect square on the left side:
(w + -0.847457627)(w + -0.847457627) = 0.64699798892

Calculate the square root of the right side: 0.804361852

Break this problem into two subproblems by setting 
(w + -0.847457627) equal to 0.804361852 and -0.804361852.

Subproblem 1

w + -0.847457627 = 0.804361852 Simplifying w + -0.847457627 = 0.804361852 Reorder the terms: -0.847457627 + w = 0.804361852 Solving -0.847457627 + w = 0.804361852 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.847457627' to each side of the equation. -0.847457627 + 0.847457627 + w = 0.804361852 + 0.847457627 Combine like terms: -0.847457627 + 0.847457627 = 0.000000000 0.000000000 + w = 0.804361852 + 0.847457627 w = 0.804361852 + 0.847457627 Combine like terms: 0.804361852 + 0.847457627 = 1.651819479 w = 1.651819479 Simplifying w = 1.651819479

Subproblem 2

w + -0.847457627 = -0.804361852 Simplifying w + -0.847457627 = -0.804361852 Reorder the terms: -0.847457627 + w = -0.804361852 Solving -0.847457627 + w = -0.804361852 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.847457627' to each side of the equation. -0.847457627 + 0.847457627 + w = -0.804361852 + 0.847457627 Combine like terms: -0.847457627 + 0.847457627 = 0.000000000 0.000000000 + w = -0.804361852 + 0.847457627 w = -0.804361852 + 0.847457627 Combine like terms: -0.804361852 + 0.847457627 = 0.043095775 w = 0.043095775 Simplifying w = 0.043095775

Solution

The solution to the problem is based on the solutions from the subproblems. w = {1.651819479, 0.043095775}

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