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Simplifying w2 + -35w + 50 = 0 Reorder the terms: 50 + -35w + w2 = 0 Solving 50 + -35w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -35w + -50 + w2 = 0 + -50 Reorder the terms: 50 + -50 + -35w + w2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -35w + w2 = 0 + -50 -35w + w2 = 0 + -50 Combine like terms: 0 + -50 = -50 -35w + w2 = -50 The w term is -35w. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35w + 306.25 + w2 = -50 + 306.25 Reorder the terms: 306.25 + -35w + w2 = -50 + 306.25 Combine like terms: -50 + 306.25 = 256.25 306.25 + -35w + w2 = 256.25 Factor a perfect square on the left side: (w + -17.5)(w + -17.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (w + -17.5) equal to 16.007810594 and -16.007810594.Subproblem 1
w + -17.5 = 16.007810594 Simplifying w + -17.5 = 16.007810594 Reorder the terms: -17.5 + w = 16.007810594 Solving -17.5 + w = 16.007810594 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + w = 16.007810594 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + w = 16.007810594 + 17.5 w = 16.007810594 + 17.5 Combine like terms: 16.007810594 + 17.5 = 33.507810594 w = 33.507810594 Simplifying w = 33.507810594Subproblem 2
w + -17.5 = -16.007810594 Simplifying w + -17.5 = -16.007810594 Reorder the terms: -17.5 + w = -16.007810594 Solving -17.5 + w = -16.007810594 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + w = -16.007810594 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + w = -16.007810594 + 17.5 w = -16.007810594 + 17.5 Combine like terms: -16.007810594 + 17.5 = 1.492189406 w = 1.492189406 Simplifying w = 1.492189406Solution
The solution to the problem is based on the solutions from the subproblems. w = {33.507810594, 1.492189406}
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