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Simplifying w2 + w + -0.2 = 0 Reorder the terms: -0.2 + w + w2 = 0 Solving -0.2 + w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + w + 0.2 + w2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + w + w2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + w + w2 = 0 + 0.2 w + w2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 w + w2 = 0.2 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = 0.2 + 0.25 Reorder the terms: 0.25 + w + w2 = 0.2 + 0.25 Combine like terms: 0.2 + 0.25 = 0.45 0.25 + w + w2 = 0.45 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (w + 0.5) equal to 0.670820393 and -0.670820393.Subproblem 1
w + 0.5 = 0.670820393 Simplifying w + 0.5 = 0.670820393 Reorder the terms: 0.5 + w = 0.670820393 Solving 0.5 + w = 0.670820393 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 0.670820393 + -0.5 w = 0.670820393 + -0.5 Combine like terms: 0.670820393 + -0.5 = 0.170820393 w = 0.170820393 Simplifying w = 0.170820393Subproblem 2
w + 0.5 = -0.670820393 Simplifying w + 0.5 = -0.670820393 Reorder the terms: 0.5 + w = -0.670820393 Solving 0.5 + w = -0.670820393 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -0.670820393 + -0.5 w = -0.670820393 + -0.5 Combine like terms: -0.670820393 + -0.5 = -1.170820393 w = -1.170820393 Simplifying w = -1.170820393Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.170820393, -1.170820393}
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