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Simplifying 14y5 + -4y3 + 2y = 0 Reorder the terms: 2y + -4y3 + 14y5 = 0 Solving 2y + -4y3 + 14y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(1 + -2y2 + 7y4) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(1 + -2y2 + 7y4)' equal to zero and attempt to solve: Simplifying 1 + -2y2 + 7y4 = 0 Solving 1 + -2y2 + 7y4 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -0.2857142857y2 + y4 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.2857142857y2 + -0.1428571429 + y4 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -0.2857142857y2 + y4 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -0.2857142857y2 + y4 = 0 + -0.1428571429 -0.2857142857y2 + y4 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -0.2857142857y2 + y4 = -0.1428571429 The y term is -0.2857142857y2. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857y2 + 0.02040816328 + y4 = -0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857y2 + y4 = -0.1428571429 + 0.02040816328 Combine like terms: -0.1428571429 + 0.02040816328 = -0.12244897962 0.02040816328 + -0.2857142857y2 + y4 = -0.12244897962 Factor a perfect square on the left side: (y2 + -0.1428571429)(y2 + -0.1428571429) = -0.12244897962 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
y = {0}
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