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Simplifying 3y4 + 9y2 + -15 = 0 Reorder the terms: -15 + 9y2 + 3y4 = 0 Solving -15 + 9y2 + 3y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 3y2 + y4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 3y2 + y4)' equal to zero and attempt to solve: Simplifying -5 + 3y2 + y4 = 0 Solving -5 + 3y2 + y4 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 3y2 + 5 + y4 = 0 + 5 Reorder the terms: -5 + 5 + 3y2 + y4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3y2 + y4 = 0 + 5 3y2 + y4 = 0 + 5 Combine like terms: 0 + 5 = 5 3y2 + y4 = 5 The y term is 3y2. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y2 + 2.25 + y4 = 5 + 2.25 Reorder the terms: 2.25 + 3y2 + y4 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + 3y2 + y4 = 7.25 Factor a perfect square on the left side: (y2 + 1.5)(y2 + 1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (y2 + 1.5) equal to 2.692582404 and -2.692582404.Subproblem 1
y2 + 1.5 = 2.692582404 Simplifying y2 + 1.5 = 2.692582404 Reorder the terms: 1.5 + y2 = 2.692582404 Solving 1.5 + y2 = 2.692582404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y2 = 2.692582404 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y2 = 2.692582404 + -1.5 y2 = 2.692582404 + -1.5 Combine like terms: 2.692582404 + -1.5 = 1.192582404 y2 = 1.192582404 Simplifying y2 = 1.192582404 Take the square root of each side: y = {-1.092054213, 1.092054213}Subproblem 2
y2 + 1.5 = -2.692582404 Simplifying y2 + 1.5 = -2.692582404 Reorder the terms: 1.5 + y2 = -2.692582404 Solving 1.5 + y2 = -2.692582404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y2 = -2.692582404 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y2 = -2.692582404 + -1.5 y2 = -2.692582404 + -1.5 Combine like terms: -2.692582404 + -1.5 = -4.192582404 y2 = -4.192582404 Simplifying y2 = -4.192582404 Reorder the terms: 4.192582404 + y2 = -4.192582404 + 4.192582404 Combine like terms: -4.192582404 + 4.192582404 = 0.000000000 4.192582404 + 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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