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Simplifying 2w3 + 8w2 + 5w = 0 Reorder the terms: 5w + 8w2 + 2w3 = 0 Solving 5w + 8w2 + 2w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(5 + 8w + 2w2) = 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 + 8w + 2w2)' equal to zero and attempt to solve: Simplifying 5 + 8w + 2w2 = 0 Solving 5 + 8w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 4w + w2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 4w + -2.5 + w2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 4w + w2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 4w + w2 = 0 + -2.5 4w + w2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 4w + w2 = -2.5 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 = -2.5 + 4 Reorder the terms: 4 + 4w + w2 = -2.5 + 4 Combine like terms: -2.5 + 4 = 1.5 4 + 4w + w2 = 1.5 Factor a perfect square on the left side: (w + 2)(w + 2) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (w + 2) equal to 1.224744871 and -1.224744871.Subproblem 1
w + 2 = 1.224744871 Simplifying w + 2 = 1.224744871 Reorder the terms: 2 + w = 1.224744871 Solving 2 + w = 1.224744871 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 = 1.224744871 + -2 Combine like terms: 2 + -2 = 0 0 + w = 1.224744871 + -2 w = 1.224744871 + -2 Combine like terms: 1.224744871 + -2 = -0.775255129 w = -0.775255129 Simplifying w = -0.775255129Subproblem 2
w + 2 = -1.224744871 Simplifying w + 2 = -1.224744871 Reorder the terms: 2 + w = -1.224744871 Solving 2 + w = -1.224744871 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 = -1.224744871 + -2 Combine like terms: 2 + -2 = 0 0 + w = -1.224744871 + -2 w = -1.224744871 + -2 Combine like terms: -1.224744871 + -2 = -3.224744871 w = -3.224744871 Simplifying w = -3.224744871Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.775255129, -3.224744871}Solution
w = {0, -0.775255129, -3.224744871}
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