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Simplifying w2 + -12w = -8 Reorder the terms: -12w + w2 = -8 Solving -12w + w2 = -8 Solving for variable 'w'. Reorder the terms: 8 + -12w + w2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + -12w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -12w + -8 + w2 = 0 + -8 Reorder the terms: 8 + -8 + -12w + w2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -12w + w2 = 0 + -8 -12w + w2 = 0 + -8 Combine like terms: 0 + -8 = -8 -12w + w2 = -8 The w term is -12w. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12w + 36 + w2 = -8 + 36 Reorder the terms: 36 + -12w + w2 = -8 + 36 Combine like terms: -8 + 36 = 28 36 + -12w + w2 = 28 Factor a perfect square on the left side: (w + -6)(w + -6) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (w + -6) equal to 5.291502622 and -5.291502622.Subproblem 1
w + -6 = 5.291502622 Simplifying w + -6 = 5.291502622 Reorder the terms: -6 + w = 5.291502622 Solving -6 + w = 5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = 5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + w = 5.291502622 + 6 w = 5.291502622 + 6 Combine like terms: 5.291502622 + 6 = 11.291502622 w = 11.291502622 Simplifying w = 11.291502622Subproblem 2
w + -6 = -5.291502622 Simplifying w + -6 = -5.291502622 Reorder the terms: -6 + w = -5.291502622 Solving -6 + w = -5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = -5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + w = -5.291502622 + 6 w = -5.291502622 + 6 Combine like terms: -5.291502622 + 6 = 0.708497378 w = 0.708497378 Simplifying w = 0.708497378Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.291502622, 0.708497378}
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