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Simplifying 96 = w(w + 2) Reorder the terms: 96 = w(2 + w) 96 = (2 * w + w * w) 96 = (2w + w2) Solving 96 = 2w + w2 Solving for variable 'w'. Reorder the terms: 96 + -2w + -1w2 = 2w + -2w + w2 + -1w2 Combine like terms: 2w + -2w = 0 96 + -2w + -1w2 = 0 + w2 + -1w2 96 + -2w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 96 + -2w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -96 + 2w + w2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 2w + 96 + w2 = 0 + 96 Reorder the terms: -96 + 96 + 2w + w2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 2w + w2 = 0 + 96 2w + w2 = 0 + 96 Combine like terms: 0 + 96 = 96 2w + w2 = 96 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 96 + 1 Reorder the terms: 1 + 2w + w2 = 96 + 1 Combine like terms: 96 + 1 = 97 1 + 2w + w2 = 97 Factor a perfect square on the left side: (w + 1)(w + 1) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (w + 1) equal to 9.848857802 and -9.848857802.Subproblem 1
w + 1 = 9.848857802 Simplifying w + 1 = 9.848857802 Reorder the terms: 1 + w = 9.848857802 Solving 1 + w = 9.848857802 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 9.848857802 + -1 Combine like terms: 1 + -1 = 0 0 + w = 9.848857802 + -1 w = 9.848857802 + -1 Combine like terms: 9.848857802 + -1 = 8.848857802 w = 8.848857802 Simplifying w = 8.848857802Subproblem 2
w + 1 = -9.848857802 Simplifying w + 1 = -9.848857802 Reorder the terms: 1 + w = -9.848857802 Solving 1 + w = -9.848857802 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -9.848857802 + -1 Combine like terms: 1 + -1 = 0 0 + w = -9.848857802 + -1 w = -9.848857802 + -1 Combine like terms: -9.848857802 + -1 = -10.848857802 w = -10.848857802 Simplifying w = -10.848857802Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.848857802, -10.848857802}
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