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Simplifying y4 + 6y2 + -4 = 0 Reorder the terms: -4 + 6y2 + y4 = 0 Solving -4 + 6y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 6y2 + 4 + y4 = 0 + 4 Reorder the terms: -4 + 4 + 6y2 + y4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6y2 + y4 = 0 + 4 6y2 + y4 = 0 + 4 Combine like terms: 0 + 4 = 4 6y2 + y4 = 4 The y term is 6y2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y2 + 9 + y4 = 4 + 9 Reorder the terms: 9 + 6y2 + y4 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + 6y2 + y4 = 13 Factor a perfect square on the left side: (y2 + 3)(y2 + 3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (y2 + 3) equal to 3.605551275 and -3.605551275.Subproblem 1
y2 + 3 = 3.605551275 Simplifying y2 + 3 = 3.605551275 Reorder the terms: 3 + y2 = 3.605551275 Solving 3 + y2 = 3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y2 = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + y2 = 3.605551275 + -3 y2 = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 y2 = 0.605551275 Simplifying y2 = 0.605551275 Take the square root of each side: y = {-0.778171752, 0.778171752}Subproblem 2
y2 + 3 = -3.605551275 Simplifying y2 + 3 = -3.605551275 Reorder the terms: 3 + y2 = -3.605551275 Solving 3 + y2 = -3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y2 = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + y2 = -3.605551275 + -3 y2 = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 y2 = -6.605551275 Simplifying y2 = -6.605551275 Reorder the terms: 6.605551275 + y2 = -6.605551275 + 6.605551275 Combine like terms: -6.605551275 + 6.605551275 = 0.000000000 6.605551275 + 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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