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Simplifying 2y4 + -7y2 + 3 = 0 Reorder the terms: 3 + -7y2 + 2y4 = 0 Solving 3 + -7y2 + 2y4 = 0 Solving for variable 'y'. Factor a trinomial. (1 + -2y2)(3 + -1y2) = 0Subproblem 1
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}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 = {-0.707106781, 0.707106781, -1.732050808, 1.732050808}
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