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Simplifying 2w2 + -50w + 75 = 0 Reorder the terms: 75 + -50w + 2w2 = 0 Solving 75 + -50w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 37.5 + -25w + w2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -25w + -37.5 + w2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -25w + w2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -25w + w2 = 0 + -37.5 -25w + w2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -25w + w2 = -37.5 The w term is -25w. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25w + 156.25 + w2 = -37.5 + 156.25 Reorder the terms: 156.25 + -25w + w2 = -37.5 + 156.25 Combine like terms: -37.5 + 156.25 = 118.75 156.25 + -25w + w2 = 118.75 Factor a perfect square on the left side: (w + -12.5)(w + -12.5) = 118.75 Calculate the square root of the right side: 10.897247359 Break this problem into two subproblems by setting (w + -12.5) equal to 10.897247359 and -10.897247359.Subproblem 1
w + -12.5 = 10.897247359 Simplifying w + -12.5 = 10.897247359 Reorder the terms: -12.5 + w = 10.897247359 Solving -12.5 + w = 10.897247359 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + w = 10.897247359 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w = 10.897247359 + 12.5 w = 10.897247359 + 12.5 Combine like terms: 10.897247359 + 12.5 = 23.397247359 w = 23.397247359 Simplifying w = 23.397247359Subproblem 2
w + -12.5 = -10.897247359 Simplifying w + -12.5 = -10.897247359 Reorder the terms: -12.5 + w = -10.897247359 Solving -12.5 + w = -10.897247359 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + w = -10.897247359 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w = -10.897247359 + 12.5 w = -10.897247359 + 12.5 Combine like terms: -10.897247359 + 12.5 = 1.602752641 w = 1.602752641 Simplifying w = 1.602752641Solution
The solution to the problem is based on the solutions from the subproblems. w = {23.397247359, 1.602752641}
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