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Simplifying -1y4 + -13y2 + 36 = 0 Reorder the terms: 36 + -13y2 + -1y4 = 0 Solving 36 + -13y2 + -1y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + 13y2 + y4 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 13y2 + 36 + y4 = 0 + 36 Reorder the terms: -36 + 36 + 13y2 + y4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 13y2 + y4 = 0 + 36 13y2 + y4 = 0 + 36 Combine like terms: 0 + 36 = 36 13y2 + y4 = 36 The y term is 13y2. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13y2 + 42.25 + y4 = 36 + 42.25 Reorder the terms: 42.25 + 13y2 + y4 = 36 + 42.25 Combine like terms: 36 + 42.25 = 78.25 42.25 + 13y2 + y4 = 78.25 Factor a perfect square on the left side: (y2 + 6.5)(y2 + 6.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (y2 + 6.5) equal to 8.845903006 and -8.845903006.Subproblem 1
y2 + 6.5 = 8.845903006 Simplifying y2 + 6.5 = 8.845903006 Reorder the terms: 6.5 + y2 = 8.845903006 Solving 6.5 + y2 = 8.845903006 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + y2 = 8.845903006 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y2 = 8.845903006 + -6.5 y2 = 8.845903006 + -6.5 Combine like terms: 8.845903006 + -6.5 = 2.345903006 y2 = 2.345903006 Simplifying y2 = 2.345903006 Take the square root of each side: y = {-1.531634097, 1.531634097}Subproblem 2
y2 + 6.5 = -8.845903006 Simplifying y2 + 6.5 = -8.845903006 Reorder the terms: 6.5 + y2 = -8.845903006 Solving 6.5 + y2 = -8.845903006 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + y2 = -8.845903006 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y2 = -8.845903006 + -6.5 y2 = -8.845903006 + -6.5 Combine like terms: -8.845903006 + -6.5 = -15.345903006 y2 = -15.345903006 Simplifying y2 = -15.345903006 Reorder the terms: 15.345903006 + y2 = -15.345903006 + 15.345903006 Combine like terms: -15.345903006 + 15.345903006 = 0.000000000 15.345903006 + 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.
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