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Simplifying -4y3 + -2y5 + 2y = 0 Reorder the terms: 2y + -4y3 + -2y5 = 0 Solving 2y + -4y3 + -2y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(1 + -2y2 + -1y4) = 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 + -1y4)' equal to zero and attempt to solve: Simplifying 1 + -2y2 + -1y4 = 0 Solving 1 + -2y2 + -1y4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 2y2 + y4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2y2 + 1 + y4 = 0 + 1 Reorder the terms: -1 + 1 + 2y2 + y4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2y2 + y4 = 0 + 1 2y2 + y4 = 0 + 1 Combine like terms: 0 + 1 = 1 2y2 + y4 = 1 The y term is 2y2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y2 + 1 + y4 = 1 + 1 Reorder the terms: 1 + 2y2 + y4 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2y2 + y4 = 2 Factor a perfect square on the left side: (y2 + 1)(y2 + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (y2 + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
y2 + 1 = 1.414213562 Simplifying y2 + 1 = 1.414213562 Reorder the terms: 1 + y2 = 1.414213562 Solving 1 + y2 = 1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = 1.414213562 + -1 y2 = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 y2 = 0.414213562 Simplifying y2 = 0.414213562 Take the square root of each side: y = {-0.643594253, 0.643594253}Subproblem 2
y2 + 1 = -1.414213562 Simplifying y2 + 1 = -1.414213562 Reorder the terms: 1 + y2 = -1.414213562 Solving 1 + y2 = -1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = -1.414213562 + -1 y2 = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 y2 = -2.414213562 Simplifying y2 = -2.414213562 Reorder the terms: 2.414213562 + y2 = -2.414213562 + 2.414213562 Combine like terms: -2.414213562 + 2.414213562 = 0.000000000 2.414213562 + y2 = 0.000000000 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. This subproblem is being ignored because a solution could not be determined.Solution
y = {0}
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