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Simplifying y4 + 12y2 + -2 = 0 Reorder the terms: -2 + 12y2 + y4 = 0 Solving -2 + 12y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 12y2 + 2 + y4 = 0 + 2 Reorder the terms: -2 + 2 + 12y2 + y4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 12y2 + y4 = 0 + 2 12y2 + y4 = 0 + 2 Combine like terms: 0 + 2 = 2 12y2 + y4 = 2 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 = 2 + 36 Reorder the terms: 36 + 12y2 + y4 = 2 + 36 Combine like terms: 2 + 36 = 38 36 + 12y2 + y4 = 38 Factor a perfect square on the left side: (y2 + 6)(y2 + 6) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (y2 + 6) equal to 6.164414003 and -6.164414003.Subproblem 1
y2 + 6 = 6.164414003 Simplifying y2 + 6 = 6.164414003 Reorder the terms: 6 + y2 = 6.164414003 Solving 6 + y2 = 6.164414003 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 = 6.164414003 + -6 Combine like terms: 6 + -6 = 0 0 + y2 = 6.164414003 + -6 y2 = 6.164414003 + -6 Combine like terms: 6.164414003 + -6 = 0.164414003 y2 = 0.164414003 Simplifying y2 = 0.164414003 Take the square root of each side: y = {-0.405479966, 0.405479966}Subproblem 2
y2 + 6 = -6.164414003 Simplifying y2 + 6 = -6.164414003 Reorder the terms: 6 + y2 = -6.164414003 Solving 6 + y2 = -6.164414003 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 = -6.164414003 + -6 Combine like terms: 6 + -6 = 0 0 + y2 = -6.164414003 + -6 y2 = -6.164414003 + -6 Combine like terms: -6.164414003 + -6 = -12.164414003 y2 = -12.164414003 Simplifying y2 = -12.164414003 Reorder the terms: 12.164414003 + y2 = -12.164414003 + 12.164414003 Combine like terms: -12.164414003 + 12.164414003 = 0.000000000 12.164414003 + 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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