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Simplifying 64w2 + w + -4 = 0 Reorder the terms: -4 + w + 64w2 = 0 Solving -4 + w + 64w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.0625 + 0.015625w + w2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.015625w + 0.0625 + w2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.015625w + w2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.015625w + w2 = 0 + 0.0625 0.015625w + w2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.015625w + w2 = 0.0625 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. 0.015625w + 0.25 + w2 = 0.0625 + 0.25 Reorder the terms: 0.25 + 0.015625w + w2 = 0.0625 + 0.25 Combine like terms: 0.0625 + 0.25 = 0.3125 0.25 + 0.015625w + w2 = 0.3125 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (w + 0.5) equal to 0.559016994 and -0.559016994.Subproblem 1
w + 0.5 = 0.559016994 Simplifying w + 0.5 = 0.559016994 Reorder the terms: 0.5 + w = 0.559016994 Solving 0.5 + w = 0.559016994 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 = 0.559016994 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 0.559016994 + -0.5 w = 0.559016994 + -0.5 Combine like terms: 0.559016994 + -0.5 = 0.059016994 w = 0.059016994 Simplifying w = 0.059016994Subproblem 2
w + 0.5 = -0.559016994 Simplifying w + 0.5 = -0.559016994 Reorder the terms: 0.5 + w = -0.559016994 Solving 0.5 + w = -0.559016994 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 = -0.559016994 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -0.559016994 + -0.5 w = -0.559016994 + -0.5 Combine like terms: -0.559016994 + -0.5 = -1.059016994 w = -1.059016994 Simplifying w = -1.059016994Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.059016994, -1.059016994}
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