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Simplifying 64y14 + 16y10 + 40y6 = 0 Reorder the terms: 40y6 + 16y10 + 64y14 = 0 Solving 40y6 + 16y10 + 64y14 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '8y6'. 8y6(5 + 2y4 + 8y8) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'y6' equal to zero and attempt to solve: Simplifying y6 = 0 Solving y6 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y6 = 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 '(5 + 2y4 + 8y8)' equal to zero and attempt to solve: Simplifying 5 + 2y4 + 8y8 = 0 Solving 5 + 2y4 + 8y8 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 0.25y4 + y8 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 0.25y4 + -0.625 + y8 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 0.25y4 + y8 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 0.25y4 + y8 = 0 + -0.625 0.25y4 + y8 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 0.25y4 + y8 = -0.625 The y term is 0.25y4. 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. 0.25y4 + 0.015625 + y8 = -0.625 + 0.015625 Reorder the terms: 0.015625 + 0.25y4 + y8 = -0.625 + 0.015625 Combine like terms: -0.625 + 0.015625 = -0.609375 0.015625 + 0.25y4 + y8 = -0.609375 Factor a perfect square on the left side: (y4 + 0.125)(y4 + 0.125) = -0.609375 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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