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Simplifying -1w2 + -8w + 12 = 0 Reorder the terms: 12 + -8w + -1w2 = 0 Solving 12 + -8w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 8w + w2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 8w + 12 + w2 = 0 + 12 Reorder the terms: -12 + 12 + 8w + w2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 8w + w2 = 0 + 12 8w + w2 = 0 + 12 Combine like terms: 0 + 12 = 12 8w + w2 = 12 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = 12 + 16 Reorder the terms: 16 + 8w + w2 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + 8w + w2 = 28 Factor a perfect square on the left side: (w + 4)(w + 4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (w + 4) equal to 5.291502622 and -5.291502622.Subproblem 1
w + 4 = 5.291502622 Simplifying w + 4 = 5.291502622 Reorder the terms: 4 + w = 5.291502622 Solving 4 + w = 5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + w = 5.291502622 + -4 w = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 w = 1.291502622 Simplifying w = 1.291502622Subproblem 2
w + 4 = -5.291502622 Simplifying w + 4 = -5.291502622 Reorder the terms: 4 + w = -5.291502622 Solving 4 + w = -5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + w = -5.291502622 + -4 w = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 w = -9.291502622 Simplifying w = -9.291502622Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.291502622, -9.291502622}
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