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Simplifying 2y4 + -9y2 + 1 = 0 Reorder the terms: 1 + -9y2 + 2y4 = 0 Solving 1 + -9y2 + 2y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -4.5y2 + y4 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -4.5y2 + -0.5 + y4 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -4.5y2 + y4 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -4.5y2 + y4 = 0 + -0.5 -4.5y2 + y4 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -4.5y2 + y4 = -0.5 The y term is -4.5y2. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5y2 + 5.0625 + y4 = -0.5 + 5.0625 Reorder the terms: 5.0625 + -4.5y2 + y4 = -0.5 + 5.0625 Combine like terms: -0.5 + 5.0625 = 4.5625 5.0625 + -4.5y2 + y4 = 4.5625 Factor a perfect square on the left side: (y2 + -2.25)(y2 + -2.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (y2 + -2.25) equal to 2.136000936 and -2.136000936.Subproblem 1
y2 + -2.25 = 2.136000936 Simplifying y2 + -2.25 = 2.136000936 Reorder the terms: -2.25 + y2 = 2.136000936 Solving -2.25 + y2 = 2.136000936 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y2 = 2.136000936 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y2 = 2.136000936 + 2.25 y2 = 2.136000936 + 2.25 Combine like terms: 2.136000936 + 2.25 = 4.386000936 y2 = 4.386000936 Simplifying y2 = 4.386000936 Take the square root of each side: y = {-2.094278142, 2.094278142}Subproblem 2
y2 + -2.25 = -2.136000936 Simplifying y2 + -2.25 = -2.136000936 Reorder the terms: -2.25 + y2 = -2.136000936 Solving -2.25 + y2 = -2.136000936 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y2 = -2.136000936 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y2 = -2.136000936 + 2.25 y2 = -2.136000936 + 2.25 Combine like terms: -2.136000936 + 2.25 = 0.113999064 y2 = 0.113999064 Simplifying y2 = 0.113999064 Take the square root of each side: y = {-0.337637474, 0.337637474}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.094278142, 2.094278142, -0.337637474, 0.337637474}
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