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Simplifying y4 + 18y2 + -27 = 0 Reorder the terms: -27 + 18y2 + y4 = 0 Solving -27 + 18y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 18y2 + 27 + y4 = 0 + 27 Reorder the terms: -27 + 27 + 18y2 + y4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 18y2 + y4 = 0 + 27 18y2 + y4 = 0 + 27 Combine like terms: 0 + 27 = 27 18y2 + y4 = 27 The y term is 18y2. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18y2 + 81 + y4 = 27 + 81 Reorder the terms: 81 + 18y2 + y4 = 27 + 81 Combine like terms: 27 + 81 = 108 81 + 18y2 + y4 = 108 Factor a perfect square on the left side: (y2 + 9)(y2 + 9) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (y2 + 9) equal to 10.392304845 and -10.392304845.Subproblem 1
y2 + 9 = 10.392304845 Simplifying y2 + 9 = 10.392304845 Reorder the terms: 9 + y2 = 10.392304845 Solving 9 + y2 = 10.392304845 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y2 = 10.392304845 + -9 Combine like terms: 9 + -9 = 0 0 + y2 = 10.392304845 + -9 y2 = 10.392304845 + -9 Combine like terms: 10.392304845 + -9 = 1.392304845 y2 = 1.392304845 Simplifying y2 = 1.392304845 Take the square root of each side: y = {-1.179959679, 1.179959679}Subproblem 2
y2 + 9 = -10.392304845 Simplifying y2 + 9 = -10.392304845 Reorder the terms: 9 + y2 = -10.392304845 Solving 9 + y2 = -10.392304845 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y2 = -10.392304845 + -9 Combine like terms: 9 + -9 = 0 0 + y2 = -10.392304845 + -9 y2 = -10.392304845 + -9 Combine like terms: -10.392304845 + -9 = -19.392304845 y2 = -19.392304845 Simplifying y2 = -19.392304845 Reorder the terms: 19.392304845 + y2 = -19.392304845 + 19.392304845 Combine like terms: -19.392304845 + 19.392304845 = 0.000000000 19.392304845 + 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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