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Simplifying 2x0y2 = 32y10 Solving 2y2 = 32y10 Solving for variable 'y'. Combine like terms: 32y10 + -32y10 = 0 2y2 + -32y10 = 0 Factor out the Greatest Common Factor (GCF), '2y2'. 2y2(1 + -16y8) = 0 Factor a difference between two squares. 2y2((1 + 4y4)(1 + -4y4)) = 0 Factor a difference between two squares. 2y2((1 + 4y4)((1 + 2y2)(1 + -2y2))) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(1 + 4y4)' equal to zero and attempt to solve: Simplifying 1 + 4y4 = 0 Solving 1 + 4y4 = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4y4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4y4 = 0 + -1 4y4 = 0 + -1 Combine like terms: 0 + -1 = -1 4y4 = -1 Divide each side by '4'. y4 = -0.25 Simplifying y4 = -0.25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + 2y2)' equal to zero and attempt to solve: Simplifying 1 + 2y2 = 0 Solving 1 + 2y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y2 = 0 + -1 2y2 = 0 + -1 Combine like terms: 0 + -1 = -1 2y2 = -1 Divide each side by '2'. y2 = -0.5 Simplifying y2 = -0.5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(1 + -2y2)' equal to zero and attempt to solve: Simplifying 1 + -2y2 = 0 Solving 1 + -2y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y2 = 0 + -1 -2y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2y2 = -1 Divide each side by '-2'. y2 = 0.5 Simplifying y2 = 0.5 Take the square root of each side: y = {-0.707106781, 0.707106781}Solution
y = {0, -0.707106781, 0.707106781}
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