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Simplifying 3y4 + 6y2 + 6 = 0 Reorder the terms: 6 + 6y2 + 3y4 = 0 Solving 6 + 6y2 + 3y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 2y2 + y4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + 2y2 + y4)' equal to zero and attempt to solve: Simplifying 2 + 2y2 + y4 = 0 Solving 2 + 2y2 + y4 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2y2 + -2 + y4 = 0 + -2 Reorder the terms: 2 + -2 + 2y2 + y4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2y2 + y4 = 0 + -2 2y2 + y4 = 0 + -2 Combine like terms: 0 + -2 = -2 2y2 + y4 = -2 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 = -2 + 1 Reorder the terms: 1 + 2y2 + y4 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + 2y2 + y4 = -1 Factor a perfect square on the left side: (y2 + 1)(y2 + 1) = -1 Can't calculate square root of the right side. 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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