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Simplifying 2w2 + -3w + -55 = 0 Reorder the terms: -55 + -3w + 2w2 = 0 Solving -55 + -3w + 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'. -27.5 + -1.5w + w2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + -1.5w + 27.5 + w2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + -1.5w + w2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + -1.5w + w2 = 0 + 27.5 -1.5w + w2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 -1.5w + w2 = 27.5 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 = 27.5 + 0.5625 Reorder the terms: 0.5625 + -1.5w + w2 = 27.5 + 0.5625 Combine like terms: 27.5 + 0.5625 = 28.0625 0.5625 + -1.5w + w2 = 28.0625 Factor a perfect square on the left side: (w + -0.75)(w + -0.75) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (w + -0.75) equal to 5.297405025 and -5.297405025.Subproblem 1
w + -0.75 = 5.297405025 Simplifying w + -0.75 = 5.297405025 Reorder the terms: -0.75 + w = 5.297405025 Solving -0.75 + w = 5.297405025 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 = 5.297405025 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = 5.297405025 + 0.75 w = 5.297405025 + 0.75 Combine like terms: 5.297405025 + 0.75 = 6.047405025 w = 6.047405025 Simplifying w = 6.047405025Subproblem 2
w + -0.75 = -5.297405025 Simplifying w + -0.75 = -5.297405025 Reorder the terms: -0.75 + w = -5.297405025 Solving -0.75 + w = -5.297405025 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 = -5.297405025 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = -5.297405025 + 0.75 w = -5.297405025 + 0.75 Combine like terms: -5.297405025 + 0.75 = -4.547405025 w = -4.547405025 Simplifying w = -4.547405025Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.047405025, -4.547405025}
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