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Simplifying 3w2 + -6w + -81 = 0 Reorder the terms: -81 + -6w + 3w2 = 0 Solving -81 + -6w + 3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + -2w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-27 + -2w + w2)' equal to zero and attempt to solve: Simplifying -27 + -2w + w2 = 0 Solving -27 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -2w + 27 + w2 = 0 + 27 Reorder the terms: -27 + 27 + -2w + w2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -2w + w2 = 0 + 27 -2w + w2 = 0 + 27 Combine like terms: 0 + 27 = 27 -2w + w2 = 27 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 = 27 + 1 Reorder the terms: 1 + -2w + w2 = 27 + 1 Combine like terms: 27 + 1 = 28 1 + -2w + w2 = 28 Factor a perfect square on the left side: (w + -1)(w + -1) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (w + -1) equal to 5.291502622 and -5.291502622.Subproblem 1
w + -1 = 5.291502622 Simplifying w + -1 = 5.291502622 Reorder the terms: -1 + w = 5.291502622 Solving -1 + w = 5.291502622 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 = 5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + w = 5.291502622 + 1 w = 5.291502622 + 1 Combine like terms: 5.291502622 + 1 = 6.291502622 w = 6.291502622 Simplifying w = 6.291502622Subproblem 2
w + -1 = -5.291502622 Simplifying w + -1 = -5.291502622 Reorder the terms: -1 + w = -5.291502622 Solving -1 + w = -5.291502622 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 = -5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + w = -5.291502622 + 1 w = -5.291502622 + 1 Combine like terms: -5.291502622 + 1 = -4.291502622 w = -4.291502622 Simplifying w = -4.291502622Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.291502622, -4.291502622}Solution
w = {6.291502622, -4.291502622}
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