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Simplifying 2w2 + 11w + 15 = w2 + 9 Reorder the terms: 15 + 11w + 2w2 = w2 + 9 Reorder the terms: 15 + 11w + 2w2 = 9 + w2 Solving 15 + 11w + 2w2 = 9 + w2 Solving for variable 'w'. Reorder the terms: 15 + -9 + 11w + 2w2 + -1w2 = 9 + w2 + -9 + -1w2 Combine like terms: 15 + -9 = 6 6 + 11w + 2w2 + -1w2 = 9 + w2 + -9 + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 6 + 11w + 1w2 = 9 + w2 + -9 + -1w2 Reorder the terms: 6 + 11w + 1w2 = 9 + -9 + w2 + -1w2 Combine like terms: 9 + -9 = 0 6 + 11w + 1w2 = 0 + w2 + -1w2 6 + 11w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 6 + 11w + 1w2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 11w + -6 + w2 = 0 + -6 Reorder the terms: 6 + -6 + 11w + w2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 11w + w2 = 0 + -6 11w + w2 = 0 + -6 Combine like terms: 0 + -6 = -6 11w + w2 = -6 The w term is 11w. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11w + 30.25 + w2 = -6 + 30.25 Reorder the terms: 30.25 + 11w + w2 = -6 + 30.25 Combine like terms: -6 + 30.25 = 24.25 30.25 + 11w + w2 = 24.25 Factor a perfect square on the left side: (w + 5.5)(w + 5.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (w + 5.5) equal to 4.924428901 and -4.924428901.Subproblem 1
w + 5.5 = 4.924428901 Simplifying w + 5.5 = 4.924428901 Reorder the terms: 5.5 + w = 4.924428901 Solving 5.5 + w = 4.924428901 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + w = 4.924428901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = 4.924428901 + -5.5 w = 4.924428901 + -5.5 Combine like terms: 4.924428901 + -5.5 = -0.575571099 w = -0.575571099 Simplifying w = -0.575571099Subproblem 2
w + 5.5 = -4.924428901 Simplifying w + 5.5 = -4.924428901 Reorder the terms: 5.5 + w = -4.924428901 Solving 5.5 + w = -4.924428901 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + w = -4.924428901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = -4.924428901 + -5.5 w = -4.924428901 + -5.5 Combine like terms: -4.924428901 + -5.5 = -10.424428901 w = -10.424428901 Simplifying w = -10.424428901Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.575571099, -10.424428901}
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