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Simplifying 2w2 + -3w = 72 Reorder the terms: -3w + 2w2 = 72 Solving -3w + 2w2 = 72 Solving for variable 'w'. Reorder the terms: -72 + -3w + 2w2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + -3w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36 + -1.5w + w2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -1.5w + 36 + w2 = 0 + 36 Reorder the terms: -36 + 36 + -1.5w + w2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1.5w + w2 = 0 + 36 -1.5w + w2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1.5w + w2 = 36 The w term is -1.5w. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5w + 0.5625 + w2 = 36 + 0.5625 Reorder the terms: 0.5625 + -1.5w + w2 = 36 + 0.5625 Combine like terms: 36 + 0.5625 = 36.5625 0.5625 + -1.5w + w2 = 36.5625 Factor a perfect square on the left side: (w + -0.75)(w + -0.75) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (w + -0.75) equal to 6.046693311 and -6.046693311.Subproblem 1
w + -0.75 = 6.046693311 Simplifying w + -0.75 = 6.046693311 Reorder the terms: -0.75 + w = 6.046693311 Solving -0.75 + w = 6.046693311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w = 6.046693311 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = 6.046693311 + 0.75 w = 6.046693311 + 0.75 Combine like terms: 6.046693311 + 0.75 = 6.796693311 w = 6.796693311 Simplifying w = 6.796693311Subproblem 2
w + -0.75 = -6.046693311 Simplifying w + -0.75 = -6.046693311 Reorder the terms: -0.75 + w = -6.046693311 Solving -0.75 + w = -6.046693311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w = -6.046693311 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = -6.046693311 + 0.75 w = -6.046693311 + 0.75 Combine like terms: -6.046693311 + 0.75 = -5.296693311 w = -5.296693311 Simplifying w = -5.296693311Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.796693311, -5.296693311}
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