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Simplifying 2w2 + -6w + -87 = 0 Reorder the terms: -87 + -6w + 2w2 = 0 Solving -87 + -6w + 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'. -43.5 + -3w + w2 = 0 Move the constant term to the right: Add '43.5' to each side of the equation. -43.5 + -3w + 43.5 + w2 = 0 + 43.5 Reorder the terms: -43.5 + 43.5 + -3w + w2 = 0 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + -3w + w2 = 0 + 43.5 -3w + w2 = 0 + 43.5 Combine like terms: 0 + 43.5 = 43.5 -3w + w2 = 43.5 The w term is -3w. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3w + 2.25 + w2 = 43.5 + 2.25 Reorder the terms: 2.25 + -3w + w2 = 43.5 + 2.25 Combine like terms: 43.5 + 2.25 = 45.75 2.25 + -3w + w2 = 45.75 Factor a perfect square on the left side: (w + -1.5)(w + -1.5) = 45.75 Calculate the square root of the right side: 6.763874629 Break this problem into two subproblems by setting (w + -1.5) equal to 6.763874629 and -6.763874629.Subproblem 1
w + -1.5 = 6.763874629 Simplifying w + -1.5 = 6.763874629 Reorder the terms: -1.5 + w = 6.763874629 Solving -1.5 + w = 6.763874629 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = 6.763874629 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = 6.763874629 + 1.5 w = 6.763874629 + 1.5 Combine like terms: 6.763874629 + 1.5 = 8.263874629 w = 8.263874629 Simplifying w = 8.263874629Subproblem 2
w + -1.5 = -6.763874629 Simplifying w + -1.5 = -6.763874629 Reorder the terms: -1.5 + w = -6.763874629 Solving -1.5 + w = -6.763874629 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = -6.763874629 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = -6.763874629 + 1.5 w = -6.763874629 + 1.5 Combine like terms: -6.763874629 + 1.5 = -5.263874629 w = -5.263874629 Simplifying w = -5.263874629Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.263874629, -5.263874629}
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