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Simplifying w3 + 14w2 + 9w = 0 Reorder the terms: 9w + 14w2 + w3 = 0 Solving 9w + 14w2 + w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(9 + 14w + w2) = 0Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(9 + 14w + w2)' equal to zero and attempt to solve: Simplifying 9 + 14w + w2 = 0 Solving 9 + 14w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 14w + -9 + w2 = 0 + -9 Reorder the terms: 9 + -9 + 14w + w2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 14w + w2 = 0 + -9 14w + w2 = 0 + -9 Combine like terms: 0 + -9 = -9 14w + w2 = -9 The w term is 14w. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14w + 49 + w2 = -9 + 49 Reorder the terms: 49 + 14w + w2 = -9 + 49 Combine like terms: -9 + 49 = 40 49 + 14w + w2 = 40 Factor a perfect square on the left side: (w + 7)(w + 7) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (w + 7) equal to 6.32455532 and -6.32455532.Subproblem 1
w + 7 = 6.32455532 Simplifying w + 7 = 6.32455532 Reorder the terms: 7 + w = 6.32455532 Solving 7 + w = 6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + w = 6.32455532 + -7 Combine like terms: 7 + -7 = 0 0 + w = 6.32455532 + -7 w = 6.32455532 + -7 Combine like terms: 6.32455532 + -7 = -0.67544468 w = -0.67544468 Simplifying w = -0.67544468Subproblem 2
w + 7 = -6.32455532 Simplifying w + 7 = -6.32455532 Reorder the terms: 7 + w = -6.32455532 Solving 7 + w = -6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + w = -6.32455532 + -7 Combine like terms: 7 + -7 = 0 0 + w = -6.32455532 + -7 w = -6.32455532 + -7 Combine like terms: -6.32455532 + -7 = -13.32455532 w = -13.32455532 Simplifying w = -13.32455532Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.67544468, -13.32455532}Solution
w = {0, -0.67544468, -13.32455532}
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