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Simplifying 2y4 + -9y2 + 2 = 0 Reorder the terms: 2 + -9y2 + 2y4 = 0 Solving 2 + -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'. 1 + -4.5y2 + y4 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.5y2 + -1 + y4 = 0 + -1 Reorder the terms: 1 + -1 + -4.5y2 + y4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.5y2 + y4 = 0 + -1 -4.5y2 + y4 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.5y2 + y4 = -1 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 = -1 + 5.0625 Reorder the terms: 5.0625 + -4.5y2 + y4 = -1 + 5.0625 Combine like terms: -1 + 5.0625 = 4.0625 5.0625 + -4.5y2 + y4 = 4.0625 Factor a perfect square on the left side: (y2 + -2.25)(y2 + -2.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (y2 + -2.25) equal to 2.015564437 and -2.015564437.Subproblem 1
y2 + -2.25 = 2.015564437 Simplifying y2 + -2.25 = 2.015564437 Reorder the terms: -2.25 + y2 = 2.015564437 Solving -2.25 + y2 = 2.015564437 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 = 2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y2 = 2.015564437 + 2.25 y2 = 2.015564437 + 2.25 Combine like terms: 2.015564437 + 2.25 = 4.265564437 y2 = 4.265564437 Simplifying y2 = 4.265564437 Take the square root of each side: y = {-2.065324293, 2.065324293}Subproblem 2
y2 + -2.25 = -2.015564437 Simplifying y2 + -2.25 = -2.015564437 Reorder the terms: -2.25 + y2 = -2.015564437 Solving -2.25 + y2 = -2.015564437 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 = -2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y2 = -2.015564437 + 2.25 y2 = -2.015564437 + 2.25 Combine like terms: -2.015564437 + 2.25 = 0.234435563 y2 = 0.234435563 Simplifying y2 = 0.234435563 Take the square root of each side: y = {-0.484185463, 0.484185463}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.065324293, 2.065324293, -0.484185463, 0.484185463}
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