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Simplifying 16 + y4 + -12y2 = 0 Reorder the terms: 16 + -12y2 + y4 = 0 Solving 16 + -12y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -12y2 + -16 + y4 = 0 + -16 Reorder the terms: 16 + -16 + -12y2 + y4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -12y2 + y4 = 0 + -16 -12y2 + y4 = 0 + -16 Combine like terms: 0 + -16 = -16 -12y2 + y4 = -16 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 = -16 + 36 Reorder the terms: 36 + -12y2 + y4 = -16 + 36 Combine like terms: -16 + 36 = 20 36 + -12y2 + y4 = 20 Factor a perfect square on the left side: (y2 + -6)(y2 + -6) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (y2 + -6) equal to 4.472135955 and -4.472135955.Subproblem 1
y2 + -6 = 4.472135955 Simplifying y2 + -6 = 4.472135955 Reorder the terms: -6 + y2 = 4.472135955 Solving -6 + y2 = 4.472135955 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 = 4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + y2 = 4.472135955 + 6 y2 = 4.472135955 + 6 Combine like terms: 4.472135955 + 6 = 10.472135955 y2 = 10.472135955 Simplifying y2 = 10.472135955 Take the square root of each side: y = {-3.236067978, 3.236067978}Subproblem 2
y2 + -6 = -4.472135955 Simplifying y2 + -6 = -4.472135955 Reorder the terms: -6 + y2 = -4.472135955 Solving -6 + y2 = -4.472135955 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 = -4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + y2 = -4.472135955 + 6 y2 = -4.472135955 + 6 Combine like terms: -4.472135955 + 6 = 1.527864045 y2 = 1.527864045 Simplifying y2 = 1.527864045 Take the square root of each side: y = {-1.236067978, 1.236067978}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.236067978, 3.236067978, -1.236067978, 1.236067978}
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