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Simplifying 9y4 + 12y2 + 1 = 0 Reorder the terms: 1 + 12y2 + 9y4 = 0 Solving 1 + 12y2 + 9y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 1.333333333y2 + y4 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 1.333333333y2 + -0.1111111111 + y4 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 1.333333333y2 + y4 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 1.333333333y2 + y4 = 0 + -0.1111111111 1.333333333y2 + y4 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 1.333333333y2 + y4 = -0.1111111111 The y term is 1.333333333y2. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333y2 + 0.4444444442 + y4 = -0.1111111111 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333y2 + y4 = -0.1111111111 + 0.4444444442 Combine like terms: -0.1111111111 + 0.4444444442 = 0.3333333331 0.4444444442 + 1.333333333y2 + y4 = 0.3333333331 Factor a perfect square on the left side: (y2 + 0.6666666665)(y2 + 0.6666666665) = 0.3333333331 Calculate the square root of the right side: 0.577350269 Break this problem into two subproblems by setting (y2 + 0.6666666665) equal to 0.577350269 and -0.577350269.Subproblem 1
y2 + 0.6666666665 = 0.577350269 Simplifying y2 + 0.6666666665 = 0.577350269 Reorder the terms: 0.6666666665 + y2 = 0.577350269 Solving 0.6666666665 + y2 = 0.577350269 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + y2 = 0.577350269 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y2 = 0.577350269 + -0.6666666665 y2 = 0.577350269 + -0.6666666665 Combine like terms: 0.577350269 + -0.6666666665 = -0.0893163975 y2 = -0.0893163975 Simplifying y2 = -0.0893163975 Reorder the terms: 0.0893163975 + y2 = -0.0893163975 + 0.0893163975 Combine like terms: -0.0893163975 + 0.0893163975 = 0.0000000000 0.0893163975 + y2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
y2 + 0.6666666665 = -0.577350269 Simplifying y2 + 0.6666666665 = -0.577350269 Reorder the terms: 0.6666666665 + y2 = -0.577350269 Solving 0.6666666665 + y2 = -0.577350269 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + y2 = -0.577350269 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y2 = -0.577350269 + -0.6666666665 y2 = -0.577350269 + -0.6666666665 Combine like terms: -0.577350269 + -0.6666666665 = -1.2440169355 y2 = -1.2440169355 Simplifying y2 = -1.2440169355 Reorder the terms: 1.2440169355 + y2 = -1.2440169355 + 1.2440169355 Combine like terms: -1.2440169355 + 1.2440169355 = 0.0000000000 1.2440169355 + y2 = 0.0000000000 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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