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Simplifying 2w2 + 8w + -72 = 0 Reorder the terms: -72 + 8w + 2w2 = 0 Solving -72 + 8w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 4w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + 4w + w2)' equal to zero and attempt to solve: Simplifying -36 + 4w + w2 = 0 Solving -36 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 4w + 36 + w2 = 0 + 36 Reorder the terms: -36 + 36 + 4w + w2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 4w + w2 = 0 + 36 4w + w2 = 0 + 36 Combine like terms: 0 + 36 = 36 4w + w2 = 36 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 36 + 4 Reorder the terms: 4 + 4w + w2 = 36 + 4 Combine like terms: 36 + 4 = 40 4 + 4w + w2 = 40 Factor a perfect square on the left side: (w + 2)(w + 2) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (w + 2) equal to 6.32455532 and -6.32455532.Subproblem 1
w + 2 = 6.32455532 Simplifying w + 2 = 6.32455532 Reorder the terms: 2 + w = 6.32455532 Solving 2 + w = 6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + w = 6.32455532 + -2 w = 6.32455532 + -2 Combine like terms: 6.32455532 + -2 = 4.32455532 w = 4.32455532 Simplifying w = 4.32455532Subproblem 2
w + 2 = -6.32455532 Simplifying w + 2 = -6.32455532 Reorder the terms: 2 + w = -6.32455532 Solving 2 + w = -6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + w = -6.32455532 + -2 w = -6.32455532 + -2 Combine like terms: -6.32455532 + -2 = -8.32455532 w = -8.32455532 Simplifying w = -8.32455532Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.32455532, -8.32455532}Solution
w = {4.32455532, -8.32455532}
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