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Simplifying y4 + -8 + 5y2 = 0 Reorder the terms: -8 + 5y2 + y4 = 0 Solving -8 + 5y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 5y2 + 8 + y4 = 0 + 8 Reorder the terms: -8 + 8 + 5y2 + y4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5y2 + y4 = 0 + 8 5y2 + y4 = 0 + 8 Combine like terms: 0 + 8 = 8 5y2 + y4 = 8 The y term is 5y2. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5y2 + 6.25 + y4 = 8 + 6.25 Reorder the terms: 6.25 + 5y2 + y4 = 8 + 6.25 Combine like terms: 8 + 6.25 = 14.25 6.25 + 5y2 + y4 = 14.25 Factor a perfect square on the left side: (y2 + 2.5)(y2 + 2.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (y2 + 2.5) equal to 3.774917218 and -3.774917218.Subproblem 1
y2 + 2.5 = 3.774917218 Simplifying y2 + 2.5 = 3.774917218 Reorder the terms: 2.5 + y2 = 3.774917218 Solving 2.5 + y2 = 3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y2 = 3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y2 = 3.774917218 + -2.5 y2 = 3.774917218 + -2.5 Combine like terms: 3.774917218 + -2.5 = 1.274917218 y2 = 1.274917218 Simplifying y2 = 1.274917218 Take the square root of each side: y = {-1.129122322, 1.129122322}Subproblem 2
y2 + 2.5 = -3.774917218 Simplifying y2 + 2.5 = -3.774917218 Reorder the terms: 2.5 + y2 = -3.774917218 Solving 2.5 + y2 = -3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y2 = -3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y2 = -3.774917218 + -2.5 y2 = -3.774917218 + -2.5 Combine like terms: -3.774917218 + -2.5 = -6.274917218 y2 = -6.274917218 Simplifying y2 = -6.274917218 Reorder the terms: 6.274917218 + y2 = -6.274917218 + 6.274917218 Combine like terms: -6.274917218 + 6.274917218 = 0.000000000 6.274917218 + 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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