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Simplifying 2y4 + 4y2 + -12 = 0 Reorder the terms: -12 + 4y2 + 2y4 = 0 Solving -12 + 4y2 + 2y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 2y2 + y4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 2y2 + y4)' equal to zero and attempt to solve: Simplifying -6 + 2y2 + y4 = 0 Solving -6 + 2y2 + y4 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 2y2 + 6 + y4 = 0 + 6 Reorder the terms: -6 + 6 + 2y2 + y4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2y2 + y4 = 0 + 6 2y2 + y4 = 0 + 6 Combine like terms: 0 + 6 = 6 2y2 + y4 = 6 The y term is 2y2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y2 + 1 + y4 = 6 + 1 Reorder the terms: 1 + 2y2 + y4 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + 2y2 + y4 = 7 Factor a perfect square on the left side: (y2 + 1)(y2 + 1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y2 + 1) equal to 2.645751311 and -2.645751311.Subproblem 1
y2 + 1 = 2.645751311 Simplifying y2 + 1 = 2.645751311 Reorder the terms: 1 + y2 = 2.645751311 Solving 1 + y2 = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = 2.645751311 + -1 y2 = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 y2 = 1.645751311 Simplifying y2 = 1.645751311 Take the square root of each side: y = {-1.282868392, 1.282868392}Subproblem 2
y2 + 1 = -2.645751311 Simplifying y2 + 1 = -2.645751311 Reorder the terms: 1 + y2 = -2.645751311 Solving 1 + y2 = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = -2.645751311 + -1 y2 = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 y2 = -3.645751311 Simplifying y2 = -3.645751311 Reorder the terms: 3.645751311 + y2 = -3.645751311 + 3.645751311 Combine like terms: -3.645751311 + 3.645751311 = 0.000000000 3.645751311 + 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. 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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