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Simplifying w(2w + -8) = 179 Reorder the terms: w(-8 + 2w) = 179 (-8 * w + 2w * w) = 179 (-8w + 2w2) = 179 Solving -8w + 2w2 = 179 Solving for variable 'w'. Reorder the terms: -179 + -8w + 2w2 = 179 + -179 Combine like terms: 179 + -179 = 0 -179 + -8w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -89.5 + -4w + w2 = 0 Move the constant term to the right: Add '89.5' to each side of the equation. -89.5 + -4w + 89.5 + w2 = 0 + 89.5 Reorder the terms: -89.5 + 89.5 + -4w + w2 = 0 + 89.5 Combine like terms: -89.5 + 89.5 = 0.0 0.0 + -4w + w2 = 0 + 89.5 -4w + w2 = 0 + 89.5 Combine like terms: 0 + 89.5 = 89.5 -4w + w2 = 89.5 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 89.5 + 4 Reorder the terms: 4 + -4w + w2 = 89.5 + 4 Combine like terms: 89.5 + 4 = 93.5 4 + -4w + w2 = 93.5 Factor a perfect square on the left side: (w + -2)(w + -2) = 93.5 Calculate the square root of the right side: 9.669539803 Break this problem into two subproblems by setting (w + -2) equal to 9.669539803 and -9.669539803.Subproblem 1
w + -2 = 9.669539803 Simplifying w + -2 = 9.669539803 Reorder the terms: -2 + w = 9.669539803 Solving -2 + w = 9.669539803 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 9.669539803 + 2 Combine like terms: -2 + 2 = 0 0 + w = 9.669539803 + 2 w = 9.669539803 + 2 Combine like terms: 9.669539803 + 2 = 11.669539803 w = 11.669539803 Simplifying w = 11.669539803Subproblem 2
w + -2 = -9.669539803 Simplifying w + -2 = -9.669539803 Reorder the terms: -2 + w = -9.669539803 Solving -2 + w = -9.669539803 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -9.669539803 + 2 Combine like terms: -2 + 2 = 0 0 + w = -9.669539803 + 2 w = -9.669539803 + 2 Combine like terms: -9.669539803 + 2 = -7.669539803 w = -7.669539803 Simplifying w = -7.669539803Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.669539803, -7.669539803}
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