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Simplifying 2w2 + -3w + -279 = 0 Reorder the terms: -279 + -3w + 2w2 = 0 Solving -279 + -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'. -139.5 + -1.5w + w2 = 0 Move the constant term to the right: Add '139.5' to each side of the equation. -139.5 + -1.5w + 139.5 + w2 = 0 + 139.5 Reorder the terms: -139.5 + 139.5 + -1.5w + w2 = 0 + 139.5 Combine like terms: -139.5 + 139.5 = 0.0 0.0 + -1.5w + w2 = 0 + 139.5 -1.5w + w2 = 0 + 139.5 Combine like terms: 0 + 139.5 = 139.5 -1.5w + w2 = 139.5 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 = 139.5 + 0.5625 Reorder the terms: 0.5625 + -1.5w + w2 = 139.5 + 0.5625 Combine like terms: 139.5 + 0.5625 = 140.0625 0.5625 + -1.5w + w2 = 140.0625 Factor a perfect square on the left side: (w + -0.75)(w + -0.75) = 140.0625 Calculate the square root of the right side: 11.834800379 Break this problem into two subproblems by setting (w + -0.75) equal to 11.834800379 and -11.834800379.Subproblem 1
w + -0.75 = 11.834800379 Simplifying w + -0.75 = 11.834800379 Reorder the terms: -0.75 + w = 11.834800379 Solving -0.75 + w = 11.834800379 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 = 11.834800379 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = 11.834800379 + 0.75 w = 11.834800379 + 0.75 Combine like terms: 11.834800379 + 0.75 = 12.584800379 w = 12.584800379 Simplifying w = 12.584800379Subproblem 2
w + -0.75 = -11.834800379 Simplifying w + -0.75 = -11.834800379 Reorder the terms: -0.75 + w = -11.834800379 Solving -0.75 + w = -11.834800379 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 = -11.834800379 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = -11.834800379 + 0.75 w = -11.834800379 + 0.75 Combine like terms: -11.834800379 + 0.75 = -11.084800379 w = -11.084800379 Simplifying w = -11.084800379Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.584800379, -11.084800379}
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