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Simplifying w4 + 9w3 + 29w2 = 0 Reorder the terms: 29w2 + 9w3 + w4 = 0 Solving 29w2 + 9w3 + w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w2'. w2(29 + 9w + w2) = 0Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve: Simplifying w2 = 0 Solving w2 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w2 = 0 Take the square root of each side: w = {0}Subproblem 2
Set the factor '(29 + 9w + w2)' equal to zero and attempt to solve: Simplifying 29 + 9w + w2 = 0 Solving 29 + 9w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 9w + -29 + w2 = 0 + -29 Reorder the terms: 29 + -29 + 9w + w2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 9w + w2 = 0 + -29 9w + w2 = 0 + -29 Combine like terms: 0 + -29 = -29 9w + w2 = -29 The w term is 9w. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9w + 20.25 + w2 = -29 + 20.25 Reorder the terms: 20.25 + 9w + w2 = -29 + 20.25 Combine like terms: -29 + 20.25 = -8.75 20.25 + 9w + w2 = -8.75 Factor a perfect square on the left side: (w + 4.5)(w + 4.5) = -8.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
w = {0}
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