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Simplifying w5 + -6w4 + 15w3 = 0 Reorder the terms: 15w3 + -6w4 + w5 = 0 Solving 15w3 + -6w4 + w5 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w3'. w3(15 + -6w + w2) = 0Subproblem 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 '(15 + -6w + w2)' equal to zero and attempt to solve: Simplifying 15 + -6w + w2 = 0 Solving 15 + -6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -6w + -15 + w2 = 0 + -15 Reorder the terms: 15 + -15 + -6w + w2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -6w + w2 = 0 + -15 -6w + w2 = 0 + -15 Combine like terms: 0 + -15 = -15 -6w + w2 = -15 The w term is -6w. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6w + 9 + w2 = -15 + 9 Reorder the terms: 9 + -6w + w2 = -15 + 9 Combine like terms: -15 + 9 = -6 9 + -6w + w2 = -6 Factor a perfect square on the left side: (w + -3)(w + -3) = -6 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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