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Simplifying 246y4 + 580y2 + 9 = 0 Reorder the terms: 9 + 580y2 + 246y4 = 0 Solving 9 + 580y2 + 246y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 246 the coefficient of the squared term: Divide each side by '246'. 0.03658536585 + 2.357723577y2 + y4 = 0 Move the constant term to the right: Add '-0.03658536585' to each side of the equation. 0.03658536585 + 2.357723577y2 + -0.03658536585 + y4 = 0 + -0.03658536585 Reorder the terms: 0.03658536585 + -0.03658536585 + 2.357723577y2 + y4 = 0 + -0.03658536585 Combine like terms: 0.03658536585 + -0.03658536585 = 0.00000000000 0.00000000000 + 2.357723577y2 + y4 = 0 + -0.03658536585 2.357723577y2 + y4 = 0 + -0.03658536585 Combine like terms: 0 + -0.03658536585 = -0.03658536585 2.357723577y2 + y4 = -0.03658536585 The y term is 2.357723577y2. Take half its coefficient (1.178861789). Square it (1.389715118) and add it to both sides. Add '1.389715118' to each side of the equation. 2.357723577y2 + 1.389715118 + y4 = -0.03658536585 + 1.389715118 Reorder the terms: 1.389715118 + 2.357723577y2 + y4 = -0.03658536585 + 1.389715118 Combine like terms: -0.03658536585 + 1.389715118 = 1.35312975215 1.389715118 + 2.357723577y2 + y4 = 1.35312975215 Factor a perfect square on the left side: (y2 + 1.178861789)(y2 + 1.178861789) = 1.35312975215 Calculate the square root of the right side: 1.163241055 Break this problem into two subproblems by setting (y2 + 1.178861789) equal to 1.163241055 and -1.163241055.Subproblem 1
y2 + 1.178861789 = 1.163241055 Simplifying y2 + 1.178861789 = 1.163241055 Reorder the terms: 1.178861789 + y2 = 1.163241055 Solving 1.178861789 + y2 = 1.163241055 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.178861789' to each side of the equation. 1.178861789 + -1.178861789 + y2 = 1.163241055 + -1.178861789 Combine like terms: 1.178861789 + -1.178861789 = 0.000000000 0.000000000 + y2 = 1.163241055 + -1.178861789 y2 = 1.163241055 + -1.178861789 Combine like terms: 1.163241055 + -1.178861789 = -0.015620734 y2 = -0.015620734 Simplifying y2 = -0.015620734 Reorder the terms: 0.015620734 + y2 = -0.015620734 + 0.015620734 Combine like terms: -0.015620734 + 0.015620734 = 0.000000000 0.015620734 + y2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
y2 + 1.178861789 = -1.163241055 Simplifying y2 + 1.178861789 = -1.163241055 Reorder the terms: 1.178861789 + y2 = -1.163241055 Solving 1.178861789 + y2 = -1.163241055 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.178861789' to each side of the equation. 1.178861789 + -1.178861789 + y2 = -1.163241055 + -1.178861789 Combine like terms: 1.178861789 + -1.178861789 = 0.000000000 0.000000000 + y2 = -1.163241055 + -1.178861789 y2 = -1.163241055 + -1.178861789 Combine like terms: -1.163241055 + -1.178861789 = -2.342102844 y2 = -2.342102844 Simplifying y2 = -2.342102844 Reorder the terms: 2.342102844 + y2 = -2.342102844 + 2.342102844 Combine like terms: -2.342102844 + 2.342102844 = 0.000000000 2.342102844 + 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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