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Simplifying y4 + 2y2 + -20 = 0 Reorder the terms: -20 + 2y2 + y4 = 0 Solving -20 + 2y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 2y2 + 20 + y4 = 0 + 20 Reorder the terms: -20 + 20 + 2y2 + y4 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2y2 + y4 = 0 + 20 2y2 + y4 = 0 + 20 Combine like terms: 0 + 20 = 20 2y2 + y4 = 20 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 = 20 + 1 Reorder the terms: 1 + 2y2 + y4 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + 2y2 + y4 = 21 Factor a perfect square on the left side: (y2 + 1)(y2 + 1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (y2 + 1) equal to 4.582575695 and -4.582575695.Subproblem 1
y2 + 1 = 4.582575695 Simplifying y2 + 1 = 4.582575695 Reorder the terms: 1 + y2 = 4.582575695 Solving 1 + y2 = 4.582575695 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 = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = 4.582575695 + -1 y2 = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 y2 = 3.582575695 Simplifying y2 = 3.582575695 Take the square root of each side: y = {-1.892769319, 1.892769319}Subproblem 2
y2 + 1 = -4.582575695 Simplifying y2 + 1 = -4.582575695 Reorder the terms: 1 + y2 = -4.582575695 Solving 1 + y2 = -4.582575695 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 = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = -4.582575695 + -1 y2 = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 y2 = -5.582575695 Simplifying y2 = -5.582575695 Reorder the terms: 5.582575695 + y2 = -5.582575695 + 5.582575695 Combine like terms: -5.582575695 + 5.582575695 = 0.000000000 5.582575695 + 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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