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Simplifying 25y4 + y2 + -0.9216 = 0 Reorder the terms: -0.9216 + y2 + 25y4 = 0 Solving -0.9216 + y2 + 25y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.036864 + 0.04y2 + y4 = 0 Move the constant term to the right: Add '0.036864' to each side of the equation. -0.036864 + 0.04y2 + 0.036864 + y4 = 0 + 0.036864 Reorder the terms: -0.036864 + 0.036864 + 0.04y2 + y4 = 0 + 0.036864 Combine like terms: -0.036864 + 0.036864 = 0.000000 0.000000 + 0.04y2 + y4 = 0 + 0.036864 0.04y2 + y4 = 0 + 0.036864 Combine like terms: 0 + 0.036864 = 0.036864 0.04y2 + y4 = 0.036864 The y term is y2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.04y2 + 0.25 + y4 = 0.036864 + 0.25 Reorder the terms: 0.25 + 0.04y2 + y4 = 0.036864 + 0.25 Combine like terms: 0.036864 + 0.25 = 0.286864 0.25 + 0.04y2 + y4 = 0.286864 Factor a perfect square on the left side: (y2 + 0.5)(y2 + 0.5) = 0.286864 Calculate the square root of the right side: 0.535596863 Break this problem into two subproblems by setting (y2 + 0.5) equal to 0.535596863 and -0.535596863.Subproblem 1
y2 + 0.5 = 0.535596863 Simplifying y2 + 0.5 = 0.535596863 Reorder the terms: 0.5 + y2 = 0.535596863 Solving 0.5 + y2 = 0.535596863 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y2 = 0.535596863 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = 0.535596863 + -0.5 y2 = 0.535596863 + -0.5 Combine like terms: 0.535596863 + -0.5 = 0.035596863 y2 = 0.035596863 Simplifying y2 = 0.035596863 Take the square root of each side: y = {-0.188671309, 0.188671309}Subproblem 2
y2 + 0.5 = -0.535596863 Simplifying y2 + 0.5 = -0.535596863 Reorder the terms: 0.5 + y2 = -0.535596863 Solving 0.5 + y2 = -0.535596863 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y2 = -0.535596863 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = -0.535596863 + -0.5 y2 = -0.535596863 + -0.5 Combine like terms: -0.535596863 + -0.5 = -1.035596863 y2 = -1.035596863 Simplifying y2 = -1.035596863 Reorder the terms: 1.035596863 + y2 = -1.035596863 + 1.035596863 Combine like terms: -1.035596863 + 1.035596863 = 0.000000000 1.035596863 + 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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