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Simplifying 2w3 + -4w2 + -24w = 0 Reorder the terms: -24w + -4w2 + 2w3 = 0 Solving -24w + -4w2 + 2w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w'. 2w(-12 + -2w + 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 '(-12 + -2w + w2)' equal to zero and attempt to solve: Simplifying -12 + -2w + w2 = 0 Solving -12 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -2w + 12 + w2 = 0 + 12 Reorder the terms: -12 + 12 + -2w + w2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2w + w2 = 0 + 12 -2w + w2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2w + w2 = 12 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 = 12 + 1 Reorder the terms: 1 + -2w + w2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + -2w + w2 = 13 Factor a perfect square on the left side: (w + -1)(w + -1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (w + -1) equal to 3.605551275 and -3.605551275.Subproblem 1
w + -1 = 3.605551275 Simplifying w + -1 = 3.605551275 Reorder the terms: -1 + w = 3.605551275 Solving -1 + w = 3.605551275 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 = 3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + w = 3.605551275 + 1 w = 3.605551275 + 1 Combine like terms: 3.605551275 + 1 = 4.605551275 w = 4.605551275 Simplifying w = 4.605551275Subproblem 2
w + -1 = -3.605551275 Simplifying w + -1 = -3.605551275 Reorder the terms: -1 + w = -3.605551275 Solving -1 + w = -3.605551275 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 = -3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + w = -3.605551275 + 1 w = -3.605551275 + 1 Combine like terms: -3.605551275 + 1 = -2.605551275 w = -2.605551275 Simplifying w = -2.605551275Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.605551275, -2.605551275}Solution
w = {0, 4.605551275, -2.605551275}
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