.42w^2-.04w=.28

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Solution for .42w^2-.04w=.28 equation:


Simplifying
0.42w2 + -0.04w = 0.28

Reorder the terms:
-0.04w + 0.42w2 = 0.28

Solving
-0.04w + 0.42w2 = 0.28

Solving for variable 'w'.

Reorder the terms:
-0.28 + -0.04w + 0.42w2 = 0.28 + -0.28

Combine like terms: 0.28 + -0.28 = 0.00
-0.28 + -0.04w + 0.42w2 = 0.00

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}

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