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Simplifying w(3w + 6) = 39 Reorder the terms: w(6 + 3w) = 39 (6 * w + 3w * w) = 39 (6w + 3w2) = 39 Solving 6w + 3w2 = 39 Solving for variable 'w'. Reorder the terms: -39 + 6w + 3w2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + 6w + 3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + 2w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + 2w + w2)' equal to zero and attempt to solve: Simplifying -13 + 2w + w2 = 0 Solving -13 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 2w + 13 + w2 = 0 + 13 Reorder the terms: -13 + 13 + 2w + w2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2w + w2 = 0 + 13 2w + w2 = 0 + 13 Combine like terms: 0 + 13 = 13 2w + w2 = 13 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 = 13 + 1 Reorder the terms: 1 + 2w + w2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + 2w + w2 = 14 Factor a perfect square on the left side: (w + 1)(w + 1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (w + 1) equal to 3.741657387 and -3.741657387.Subproblem 1
w + 1 = 3.741657387 Simplifying w + 1 = 3.741657387 Reorder the terms: 1 + w = 3.741657387 Solving 1 + w = 3.741657387 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 = 3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + w = 3.741657387 + -1 w = 3.741657387 + -1 Combine like terms: 3.741657387 + -1 = 2.741657387 w = 2.741657387 Simplifying w = 2.741657387Subproblem 2
w + 1 = -3.741657387 Simplifying w + 1 = -3.741657387 Reorder the terms: 1 + w = -3.741657387 Solving 1 + w = -3.741657387 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 = -3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + w = -3.741657387 + -1 w = -3.741657387 + -1 Combine like terms: -3.741657387 + -1 = -4.741657387 w = -4.741657387 Simplifying w = -4.741657387Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.741657387, -4.741657387}Solution
w = {2.741657387, -4.741657387}
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