3w^5-21w^4+54w^3=0

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Solution for 3w^5-21w^4+54w^3=0 equation:


Simplifying
3w5 + -21w4 + 54w3 = 0

Reorder the terms:
54w3 + -21w4 + 3w5 = 0

Solving
54w3 + -21w4 + 3w5 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w3'.
3w3(18 + -7w + w2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'w3' equal to zero and attempt to solve: Simplifying w3 = 0 Solving w3 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(18 + -7w + w2)' equal to zero and attempt to solve: Simplifying 18 + -7w + w2 = 0 Solving 18 + -7w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -7w + -18 + w2 = 0 + -18 Reorder the terms: 18 + -18 + -7w + w2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -7w + w2 = 0 + -18 -7w + w2 = 0 + -18 Combine like terms: 0 + -18 = -18 -7w + w2 = -18 The w term is -7w. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7w + 12.25 + w2 = -18 + 12.25 Reorder the terms: 12.25 + -7w + w2 = -18 + 12.25 Combine like terms: -18 + 12.25 = -5.75 12.25 + -7w + w2 = -5.75 Factor a perfect square on the left side: (w + -3.5)(w + -3.5) = -5.75 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. The solution to this equation could not be determined.

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