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Simplifying 16w16 + 4w10 + 2w4 = 0 Reorder the terms: 2w4 + 4w10 + 16w16 = 0 Solving 2w4 + 4w10 + 16w16 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w4'. 2w4(1 + 2w6 + 8w12) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'w4' equal to zero and attempt to solve: Simplifying w4 = 0 Solving w4 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w4 = 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 '(1 + 2w6 + 8w12)' equal to zero and attempt to solve: Simplifying 1 + 2w6 + 8w12 = 0 Solving 1 + 2w6 + 8w12 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 0.25w6 + w12 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 0.25w6 + -0.125 + w12 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 0.25w6 + w12 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 0.25w6 + w12 = 0 + -0.125 0.25w6 + w12 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 0.25w6 + w12 = -0.125 The w term is 0.25w6. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25w6 + 0.015625 + w12 = -0.125 + 0.015625 Reorder the terms: 0.015625 + 0.25w6 + w12 = -0.125 + 0.015625 Combine like terms: -0.125 + 0.015625 = -0.109375 0.015625 + 0.25w6 + w12 = -0.109375 Factor a perfect square on the left side: (w6 + 0.125)(w6 + 0.125) = -0.109375 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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