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Simplifying 3w2 + 6w + -117 = 0 Reorder the terms: -117 + 6w + 3w2 = 0 Solving -117 + 6w + 3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(-39 + 2w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-39 + 2w + w2)' equal to zero and attempt to solve: Simplifying -39 + 2w + w2 = 0 Solving -39 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 2w + 39 + w2 = 0 + 39 Reorder the terms: -39 + 39 + 2w + w2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 2w + w2 = 0 + 39 2w + w2 = 0 + 39 Combine like terms: 0 + 39 = 39 2w + w2 = 39 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 39 + 1 Reorder the terms: 1 + 2w + w2 = 39 + 1 Combine like terms: 39 + 1 = 40 1 + 2w + w2 = 40 Factor a perfect square on the left side: (w + 1)(w + 1) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (w + 1) equal to 6.32455532 and -6.32455532.Subproblem 1
w + 1 = 6.32455532 Simplifying w + 1 = 6.32455532 Reorder the terms: 1 + w = 6.32455532 Solving 1 + w = 6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 6.32455532 + -1 Combine like terms: 1 + -1 = 0 0 + w = 6.32455532 + -1 w = 6.32455532 + -1 Combine like terms: 6.32455532 + -1 = 5.32455532 w = 5.32455532 Simplifying w = 5.32455532Subproblem 2
w + 1 = -6.32455532 Simplifying w + 1 = -6.32455532 Reorder the terms: 1 + w = -6.32455532 Solving 1 + w = -6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -6.32455532 + -1 Combine like terms: 1 + -1 = 0 0 + w = -6.32455532 + -1 w = -6.32455532 + -1 Combine like terms: -6.32455532 + -1 = -7.32455532 w = -7.32455532 Simplifying w = -7.32455532Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.32455532, -7.32455532}Solution
w = {5.32455532, -7.32455532}
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