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Simplifying y4 + 6y2 + -1 = 0 Reorder the terms: -1 + 6y2 + y4 = 0 Solving -1 + 6y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 6y2 + 1 + y4 = 0 + 1 Reorder the terms: -1 + 1 + 6y2 + y4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6y2 + y4 = 0 + 1 6y2 + y4 = 0 + 1 Combine like terms: 0 + 1 = 1 6y2 + y4 = 1 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 = 1 + 9 Reorder the terms: 9 + 6y2 + y4 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + 6y2 + y4 = 10 Factor a perfect square on the left side: (y2 + 3)(y2 + 3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y2 + 3) equal to 3.16227766 and -3.16227766.Subproblem 1
y2 + 3 = 3.16227766 Simplifying y2 + 3 = 3.16227766 Reorder the terms: 3 + y2 = 3.16227766 Solving 3 + y2 = 3.16227766 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 = 3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + y2 = 3.16227766 + -3 y2 = 3.16227766 + -3 Combine like terms: 3.16227766 + -3 = 0.16227766 y2 = 0.16227766 Simplifying y2 = 0.16227766 Take the square root of each side: y = {-0.402837014, 0.402837014}Subproblem 2
y2 + 3 = -3.16227766 Simplifying y2 + 3 = -3.16227766 Reorder the terms: 3 + y2 = -3.16227766 Solving 3 + y2 = -3.16227766 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 = -3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + y2 = -3.16227766 + -3 y2 = -3.16227766 + -3 Combine like terms: -3.16227766 + -3 = -6.16227766 y2 = -6.16227766 Simplifying y2 = -6.16227766 Reorder the terms: 6.16227766 + y2 = -6.16227766 + 6.16227766 Combine like terms: -6.16227766 + 6.16227766 = 0.00000000 6.16227766 + y2 = 0.00000000 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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