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Simplifying 2w3 + 6w2 + -4w = 0 Reorder the terms: -4w + 6w2 + 2w3 = 0 Solving -4w + 6w2 + 2w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w'. 2w(-2 + 3w + w2) = 0 Ignore the factor 2.Subproblem 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 '(-2 + 3w + w2)' equal to zero and attempt to solve: Simplifying -2 + 3w + w2 = 0 Solving -2 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 3w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + 3w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3w + w2 = 0 + 2 3w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 3w + w2 = 2 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 2 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3w + w2 = 4.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (w + 1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
w + 1.5 = 2.061552813 Simplifying w + 1.5 = 2.061552813 Reorder the terms: 1.5 + w = 2.061552813 Solving 1.5 + w = 2.061552813 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 2.061552813 + -1.5 w = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 w = 0.561552813 Simplifying w = 0.561552813Subproblem 2
w + 1.5 = -2.061552813 Simplifying w + 1.5 = -2.061552813 Reorder the terms: 1.5 + w = -2.061552813 Solving 1.5 + w = -2.061552813 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -2.061552813 + -1.5 w = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 w = -3.561552813 Simplifying w = -3.561552813Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.561552813, -3.561552813}Solution
w = {0, 0.561552813, -3.561552813}
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