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Simplifying w3 + 6w2 + -5w = 0 Reorder the terms: -5w + 6w2 + w3 = 0 Solving -5w + 6w2 + w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(-5 + 6w + 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 '(-5 + 6w + w2)' equal to zero and attempt to solve: Simplifying -5 + 6w + w2 = 0 Solving -5 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 6w + 5 + w2 = 0 + 5 Reorder the terms: -5 + 5 + 6w + w2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6w + w2 = 0 + 5 6w + w2 = 0 + 5 Combine like terms: 0 + 5 = 5 6w + w2 = 5 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 5 + 9 Reorder the terms: 9 + 6w + w2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + 6w + w2 = 14 Factor a perfect square on the left side: (w + 3)(w + 3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (w + 3) equal to 3.741657387 and -3.741657387.Subproblem 1
w + 3 = 3.741657387 Simplifying w + 3 = 3.741657387 Reorder the terms: 3 + w = 3.741657387 Solving 3 + w = 3.741657387 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + w = 3.741657387 + -3 w = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 w = 0.741657387 Simplifying w = 0.741657387Subproblem 2
w + 3 = -3.741657387 Simplifying w + 3 = -3.741657387 Reorder the terms: 3 + w = -3.741657387 Solving 3 + w = -3.741657387 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + w = -3.741657387 + -3 w = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 w = -6.741657387 Simplifying w = -6.741657387Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.741657387, -6.741657387}Solution
w = {0, 0.741657387, -6.741657387}
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