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Simplifying y4 + -40y2 + 256 = 0 Reorder the terms: 256 + -40y2 + y4 = 0 Solving 256 + -40y2 + y4 = 0 Solving for variable 'y'. Factor a trinomial. (8 + -1y2)(32 + -1y2) = 0Subproblem 1
Set the factor '(8 + -1y2)' equal to zero and attempt to solve: Simplifying 8 + -1y2 = 0 Solving 8 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1y2 = 0 + -8 -1y2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1y2 = -8 Divide each side by '-1'. y2 = 8 Simplifying y2 = 8 Take the square root of each side: y = {-2.828427125, 2.828427125}Subproblem 2
Set the factor '(32 + -1y2)' equal to zero and attempt to solve: Simplifying 32 + -1y2 = 0 Solving 32 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + -1y2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -1y2 = 0 + -32 -1y2 = 0 + -32 Combine like terms: 0 + -32 = -32 -1y2 = -32 Divide each side by '-1'. y2 = 32 Simplifying y2 = 32 Take the square root of each side: y = {-5.656854249, 5.656854249}Solution
y = {-2.828427125, 2.828427125, -5.656854249, 5.656854249}
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