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Simplifying 27y4 + 42y2 = 5 Reorder the terms: 42y2 + 27y4 = 5 Solving 42y2 + 27y4 = 5 Solving for variable 'y'. Reorder the terms: -5 + 42y2 + 27y4 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 42y2 + 27y4 = 0 Factor a trinomial. (-5 + -3y2)(1 + -9y2) = 0 Factor a difference between two squares. (-5 + -3y2)((1 + 3y)(1 + -3y)) = 0Subproblem 1
Set the factor '(-5 + -3y2)' equal to zero and attempt to solve: Simplifying -5 + -3y2 = 0 Solving -5 + -3y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3y2 = 0 + 5 -3y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3y2 = 5 Divide each side by '-3'. y2 = -1.666666667 Simplifying y2 = -1.666666667 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 + 3y)' equal to zero and attempt to solve: Simplifying 1 + 3y = 0 Solving 1 + 3y = 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 + 3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3y = 0 + -1 3y = 0 + -1 Combine like terms: 0 + -1 = -1 3y = -1 Divide each side by '3'. y = -0.3333333333 Simplifying y = -0.3333333333Subproblem 3
Set the factor '(1 + -3y)' equal to zero and attempt to solve: Simplifying 1 + -3y = 0 Solving 1 + -3y = 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 + -3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3y = 0 + -1 -3y = 0 + -1 Combine like terms: 0 + -1 = -1 -3y = -1 Divide each side by '-3'. y = 0.3333333333 Simplifying y = 0.3333333333Solution
y = {-0.3333333333, 0.3333333333}
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