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Simplifying 4y4 + -4y2 + 1 = 0 Reorder the terms: 1 + -4y2 + 4y4 = 0 Solving 1 + -4y2 + 4y4 = 0 Solving for variable 'y'. Factor a trinomial. (1 + -2y2)(1 + -2y2) = 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 '(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 = {-0.707106781, 0.707106781, -0.707106781, 0.707106781}
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