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Simplifying 3(w + -9) + (w + 9) * w = -8 Reorder the terms: 3(-9 + w) + (w + 9) * w = -8 (-9 * 3 + w * 3) + (w + 9) * w = -8 (-27 + 3w) + (w + 9) * w = -8 Reorder the terms: -27 + 3w + (9 + w) * w = -8 Reorder the terms for easier multiplication: -27 + 3w + w(9 + w) = -8 -27 + 3w + (9 * w + w * w) = -8 -27 + 3w + (9w + w2) = -8 Combine like terms: 3w + 9w = 12w -27 + 12w + w2 = -8 Solving -27 + 12w + w2 = -8 Solving for variable 'w'. Reorder the terms: -27 + 8 + 12w + w2 = -8 + 8 Combine like terms: -27 + 8 = -19 -19 + 12w + w2 = -8 + 8 Combine like terms: -8 + 8 = 0 -19 + 12w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 12w + 19 + w2 = 0 + 19 Reorder the terms: -19 + 19 + 12w + w2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 12w + w2 = 0 + 19 12w + w2 = 0 + 19 Combine like terms: 0 + 19 = 19 12w + w2 = 19 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 = 19 + 36 Reorder the terms: 36 + 12w + w2 = 19 + 36 Combine like terms: 19 + 36 = 55 36 + 12w + w2 = 55 Factor a perfect square on the left side: (w + 6)(w + 6) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (w + 6) equal to 7.416198487 and -7.416198487.Subproblem 1
w + 6 = 7.416198487 Simplifying w + 6 = 7.416198487 Reorder the terms: 6 + w = 7.416198487 Solving 6 + w = 7.416198487 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 = 7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + w = 7.416198487 + -6 w = 7.416198487 + -6 Combine like terms: 7.416198487 + -6 = 1.416198487 w = 1.416198487 Simplifying w = 1.416198487Subproblem 2
w + 6 = -7.416198487 Simplifying w + 6 = -7.416198487 Reorder the terms: 6 + w = -7.416198487 Solving 6 + w = -7.416198487 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 = -7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + w = -7.416198487 + -6 w = -7.416198487 + -6 Combine like terms: -7.416198487 + -6 = -13.416198487 w = -13.416198487 Simplifying w = -13.416198487Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.416198487, -13.416198487}
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