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Simplifying 2w2 + -1w + -27 = 0 Reorder the terms: -27 + -1w + 2w2 = 0 Solving -27 + -1w + 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'. -13.5 + -0.5w + w2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -0.5w + 13.5 + w2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -0.5w + w2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -0.5w + w2 = 0 + 13.5 -0.5w + w2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -0.5w + w2 = 13.5 The w term is -0.5w. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5w + 0.0625 + w2 = 13.5 + 0.0625 Reorder the terms: 0.0625 + -0.5w + w2 = 13.5 + 0.0625 Combine like terms: 13.5 + 0.0625 = 13.5625 0.0625 + -0.5w + w2 = 13.5625 Factor a perfect square on the left side: (w + -0.25)(w + -0.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (w + -0.25) equal to 3.682729966 and -3.682729966.Subproblem 1
w + -0.25 = 3.682729966 Simplifying w + -0.25 = 3.682729966 Reorder the terms: -0.25 + w = 3.682729966 Solving -0.25 + w = 3.682729966 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + w = 3.682729966 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + w = 3.682729966 + 0.25 w = 3.682729966 + 0.25 Combine like terms: 3.682729966 + 0.25 = 3.932729966 w = 3.932729966 Simplifying w = 3.932729966Subproblem 2
w + -0.25 = -3.682729966 Simplifying w + -0.25 = -3.682729966 Reorder the terms: -0.25 + w = -3.682729966 Solving -0.25 + w = -3.682729966 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + w = -3.682729966 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + w = -3.682729966 + 0.25 w = -3.682729966 + 0.25 Combine like terms: -3.682729966 + 0.25 = -3.432729966 w = -3.432729966 Simplifying w = -3.432729966Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.932729966, -3.432729966}
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