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Simplifying 14w2 + 33w + -15 = 0 Reorder the terms: -15 + 33w + 14w2 = 0 Solving -15 + 33w + 14w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.071428571 + 2.357142857w + w2 = 0 Move the constant term to the right: Add '1.071428571' to each side of the equation. -1.071428571 + 2.357142857w + 1.071428571 + w2 = 0 + 1.071428571 Reorder the terms: -1.071428571 + 1.071428571 + 2.357142857w + w2 = 0 + 1.071428571 Combine like terms: -1.071428571 + 1.071428571 = 0.000000000 0.000000000 + 2.357142857w + w2 = 0 + 1.071428571 2.357142857w + w2 = 0 + 1.071428571 Combine like terms: 0 + 1.071428571 = 1.071428571 2.357142857w + w2 = 1.071428571 The w term is 2.357142857w. Take half its coefficient (1.178571429). Square it (1.389030613) and add it to both sides. Add '1.389030613' to each side of the equation. 2.357142857w + 1.389030613 + w2 = 1.071428571 + 1.389030613 Reorder the terms: 1.389030613 + 2.357142857w + w2 = 1.071428571 + 1.389030613 Combine like terms: 1.071428571 + 1.389030613 = 2.460459184 1.389030613 + 2.357142857w + w2 = 2.460459184 Factor a perfect square on the left side: (w + 1.178571429)(w + 1.178571429) = 2.460459184 Calculate the square root of the right side: 1.56858509 Break this problem into two subproblems by setting (w + 1.178571429) equal to 1.56858509 and -1.56858509.Subproblem 1
w + 1.178571429 = 1.56858509 Simplifying w + 1.178571429 = 1.56858509 Reorder the terms: 1.178571429 + w = 1.56858509 Solving 1.178571429 + w = 1.56858509 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.178571429' to each side of the equation. 1.178571429 + -1.178571429 + w = 1.56858509 + -1.178571429 Combine like terms: 1.178571429 + -1.178571429 = 0.000000000 0.000000000 + w = 1.56858509 + -1.178571429 w = 1.56858509 + -1.178571429 Combine like terms: 1.56858509 + -1.178571429 = 0.390013661 w = 0.390013661 Simplifying w = 0.390013661Subproblem 2
w + 1.178571429 = -1.56858509 Simplifying w + 1.178571429 = -1.56858509 Reorder the terms: 1.178571429 + w = -1.56858509 Solving 1.178571429 + w = -1.56858509 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.178571429' to each side of the equation. 1.178571429 + -1.178571429 + w = -1.56858509 + -1.178571429 Combine like terms: 1.178571429 + -1.178571429 = 0.000000000 0.000000000 + w = -1.56858509 + -1.178571429 w = -1.56858509 + -1.178571429 Combine like terms: -1.56858509 + -1.178571429 = -2.747156519 w = -2.747156519 Simplifying w = -2.747156519Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.390013661, -2.747156519}
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