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Simplifying -1.5w2 + 35.25w = 180 Reorder the terms: 35.25w + -1.5w2 = 180 Solving 35.25w + -1.5w2 = 180 Solving for variable 'w'. Reorder the terms: -180 + 35.25w + -1.5w2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 35.25w + -1.5w2 = 0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. 120 + -23.5w + w2 = 0 Move the constant term to the right: Add '-120' to each side of the equation. 120 + -23.5w + -120 + w2 = 0 + -120 Reorder the terms: 120 + -120 + -23.5w + w2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -23.5w + w2 = 0 + -120 -23.5w + w2 = 0 + -120 Combine like terms: 0 + -120 = -120 -23.5w + w2 = -120 The w term is -23.5w. Take half its coefficient (-11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. -23.5w + 138.0625 + w2 = -120 + 138.0625 Reorder the terms: 138.0625 + -23.5w + w2 = -120 + 138.0625 Combine like terms: -120 + 138.0625 = 18.0625 138.0625 + -23.5w + w2 = 18.0625 Factor a perfect square on the left side: (w + -11.75)(w + -11.75) = 18.0625 Calculate the square root of the right side: 4.25 Break this problem into two subproblems by setting (w + -11.75) equal to 4.25 and -4.25.Subproblem 1
w + -11.75 = 4.25 Simplifying w + -11.75 = 4.25 Reorder the terms: -11.75 + w = 4.25 Solving -11.75 + w = 4.25 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + w = 4.25 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + w = 4.25 + 11.75 w = 4.25 + 11.75 Combine like terms: 4.25 + 11.75 = 16 w = 16 Simplifying w = 16Subproblem 2
w + -11.75 = -4.25 Simplifying w + -11.75 = -4.25 Reorder the terms: -11.75 + w = -4.25 Solving -11.75 + w = -4.25 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + w = -4.25 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + w = -4.25 + 11.75 w = -4.25 + 11.75 Combine like terms: -4.25 + 11.75 = 7.5 w = 7.5 Simplifying w = 7.5Solution
The solution to the problem is based on the solutions from the subproblems. w = {16, 7.5}
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