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Simplifying 2w2 + -8w + 4 = 0 Reorder the terms: 4 + -8w + 2w2 = 0 Solving 4 + -8w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -4w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -4w + w2)' equal to zero and attempt to solve: Simplifying 2 + -4w + w2 = 0 Solving 2 + -4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + -4w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4w + w2 = 0 + -2 -4w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4w + w2 = -2 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = -2 + 4 Reorder the terms: 4 + -4w + w2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + -4w + w2 = 2 Factor a perfect square on the left side: (w + -2)(w + -2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (w + -2) equal to 1.414213562 and -1.414213562.Subproblem 1
w + -2 = 1.414213562 Simplifying w + -2 = 1.414213562 Reorder the terms: -2 + w = 1.414213562 Solving -2 + w = 1.414213562 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + w = 1.414213562 + 2 w = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 w = 3.414213562 Simplifying w = 3.414213562Subproblem 2
w + -2 = -1.414213562 Simplifying w + -2 = -1.414213562 Reorder the terms: -2 + w = -1.414213562 Solving -2 + w = -1.414213562 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + w = -1.414213562 + 2 w = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 w = 0.585786438 Simplifying w = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.414213562, 0.585786438}Solution
w = {3.414213562, 0.585786438}
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