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Simplifying y4 + 2y2 + -117 = 0 Reorder the terms: -117 + 2y2 + y4 = 0 Solving -117 + 2y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + 2y2 + 117 + y4 = 0 + 117 Reorder the terms: -117 + 117 + 2y2 + y4 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + 2y2 + y4 = 0 + 117 2y2 + y4 = 0 + 117 Combine like terms: 0 + 117 = 117 2y2 + y4 = 117 The y term is 2y2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y2 + 1 + y4 = 117 + 1 Reorder the terms: 1 + 2y2 + y4 = 117 + 1 Combine like terms: 117 + 1 = 118 1 + 2y2 + y4 = 118 Factor a perfect square on the left side: (y2 + 1)(y2 + 1) = 118 Calculate the square root of the right side: 10.862780491 Break this problem into two subproblems by setting (y2 + 1) equal to 10.862780491 and -10.862780491.Subproblem 1
y2 + 1 = 10.862780491 Simplifying y2 + 1 = 10.862780491 Reorder the terms: 1 + y2 = 10.862780491 Solving 1 + y2 = 10.862780491 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = 10.862780491 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = 10.862780491 + -1 y2 = 10.862780491 + -1 Combine like terms: 10.862780491 + -1 = 9.862780491 y2 = 9.862780491 Simplifying y2 = 9.862780491 Take the square root of each side: y = {-3.140506407, 3.140506407}Subproblem 2
y2 + 1 = -10.862780491 Simplifying y2 + 1 = -10.862780491 Reorder the terms: 1 + y2 = -10.862780491 Solving 1 + y2 = -10.862780491 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = -10.862780491 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = -10.862780491 + -1 y2 = -10.862780491 + -1 Combine like terms: -10.862780491 + -1 = -11.862780491 y2 = -11.862780491 Simplifying y2 = -11.862780491 Reorder the terms: 11.862780491 + y2 = -11.862780491 + 11.862780491 Combine like terms: -11.862780491 + 11.862780491 = 0.000000000 11.862780491 + y2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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