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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 = -35 -35 + 12w + w2 = 8 + -8 Combine like terms: 8 + -8 = 0 -35 + 12w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 12w + 35 + w2 = 0 + 35 Reorder the terms: -35 + 35 + 12w + w2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 12w + w2 = 0 + 35 12w + w2 = 0 + 35 Combine like terms: 0 + 35 = 35 12w + w2 = 35 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 = 35 + 36 Reorder the terms: 36 + 12w + w2 = 35 + 36 Combine like terms: 35 + 36 = 71 36 + 12w + w2 = 71 Factor a perfect square on the left side: (w + 6)(w + 6) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (w + 6) equal to 8.426149773 and -8.426149773.Subproblem 1
w + 6 = 8.426149773 Simplifying w + 6 = 8.426149773 Reorder the terms: 6 + w = 8.426149773 Solving 6 + w = 8.426149773 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 = 8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + w = 8.426149773 + -6 w = 8.426149773 + -6 Combine like terms: 8.426149773 + -6 = 2.426149773 w = 2.426149773 Simplifying w = 2.426149773Subproblem 2
w + 6 = -8.426149773 Simplifying w + 6 = -8.426149773 Reorder the terms: 6 + w = -8.426149773 Solving 6 + w = -8.426149773 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 = -8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + w = -8.426149773 + -6 w = -8.426149773 + -6 Combine like terms: -8.426149773 + -6 = -14.426149773 w = -14.426149773 Simplifying w = -14.426149773Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.426149773, -14.426149773}
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