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Simplifying y4 + 12y2 + 5 = 0 Reorder the terms: 5 + 12y2 + y4 = 0 Solving 5 + 12y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 12y2 + -5 + y4 = 0 + -5 Reorder the terms: 5 + -5 + 12y2 + y4 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 12y2 + y4 = 0 + -5 12y2 + y4 = 0 + -5 Combine like terms: 0 + -5 = -5 12y2 + y4 = -5 The y term is 12y2. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12y2 + 36 + y4 = -5 + 36 Reorder the terms: 36 + 12y2 + y4 = -5 + 36 Combine like terms: -5 + 36 = 31 36 + 12y2 + y4 = 31 Factor a perfect square on the left side: (y2 + 6)(y2 + 6) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (y2 + 6) equal to 5.567764363 and -5.567764363.Subproblem 1
y2 + 6 = 5.567764363 Simplifying y2 + 6 = 5.567764363 Reorder the terms: 6 + y2 = 5.567764363 Solving 6 + y2 = 5.567764363 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y2 = 5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + y2 = 5.567764363 + -6 y2 = 5.567764363 + -6 Combine like terms: 5.567764363 + -6 = -0.432235637 y2 = -0.432235637 Simplifying y2 = -0.432235637 Reorder the terms: 0.432235637 + y2 = -0.432235637 + 0.432235637 Combine like terms: -0.432235637 + 0.432235637 = 0.000000000 0.432235637 + y2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
y2 + 6 = -5.567764363 Simplifying y2 + 6 = -5.567764363 Reorder the terms: 6 + y2 = -5.567764363 Solving 6 + y2 = -5.567764363 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y2 = -5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + y2 = -5.567764363 + -6 y2 = -5.567764363 + -6 Combine like terms: -5.567764363 + -6 = -11.567764363 y2 = -11.567764363 Simplifying y2 = -11.567764363 Reorder the terms: 11.567764363 + y2 = -11.567764363 + 11.567764363 Combine like terms: -11.567764363 + 11.567764363 = 0.000000000 11.567764363 + 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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