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Simplifying y4 + -6y2 + 9 = 0 Reorder the terms: 9 + -6y2 + y4 = 0 Solving 9 + -6y2 + y4 = 0 Solving for variable 'y'. Factor a trinomial. (3 + -1y2)(3 + -1y2) = 0Subproblem 1
Set the factor '(3 + -1y2)' equal to zero and attempt to solve: Simplifying 3 + -1y2 = 0 Solving 3 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y2 = 0 + -3 -1y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1y2 = -3 Divide each side by '-1'. y2 = 3 Simplifying y2 = 3 Take the square root of each side: y = {-1.732050808, 1.732050808}Subproblem 2
Set the factor '(3 + -1y2)' equal to zero and attempt to solve: Simplifying 3 + -1y2 = 0 Solving 3 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y2 = 0 + -3 -1y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1y2 = -3 Divide each side by '-1'. y2 = 3 Simplifying y2 = 3 Take the square root of each side: y = {-1.732050808, 1.732050808}Solution
y = {-1.732050808, 1.732050808, -1.732050808, 1.732050808}
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