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Simplifying 4y4 + 8y2 + -9 = 0 Reorder the terms: -9 + 8y2 + 4y4 = 0 Solving -9 + 8y2 + 4y4 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 2y2 + y4 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 2y2 + 2.25 + y4 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 2y2 + y4 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 2y2 + y4 = 0 + 2.25 2y2 + y4 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 2y2 + y4 = 2.25 The y term is 2y2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y2 + 1 + y4 = 2.25 + 1 Reorder the terms: 1 + 2y2 + y4 = 2.25 + 1 Combine like terms: 2.25 + 1 = 3.25 1 + 2y2 + y4 = 3.25 Factor a perfect square on the left side: (y2 + 1)(y2 + 1) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (y2 + 1) equal to 1.802775638 and -1.802775638.Subproblem 1
y2 + 1 = 1.802775638 Simplifying y2 + 1 = 1.802775638 Reorder the terms: 1 + y2 = 1.802775638 Solving 1 + y2 = 1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = 1.802775638 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = 1.802775638 + -1 y2 = 1.802775638 + -1 Combine like terms: 1.802775638 + -1 = 0.802775638 y2 = 0.802775638 Simplifying y2 = 0.802775638 Take the square root of each side: y = {-0.895977476, 0.895977476}Subproblem 2
y2 + 1 = -1.802775638 Simplifying y2 + 1 = -1.802775638 Reorder the terms: 1 + y2 = -1.802775638 Solving 1 + y2 = -1.802775638 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y2 = -1.802775638 + -1 Combine like terms: 1 + -1 = 0 0 + y2 = -1.802775638 + -1 y2 = -1.802775638 + -1 Combine like terms: -1.802775638 + -1 = -2.802775638 y2 = -2.802775638 Simplifying y2 = -2.802775638 Reorder the terms: 2.802775638 + y2 = -2.802775638 + 2.802775638 Combine like terms: -2.802775638 + 2.802775638 = 0.000000000 2.802775638 + 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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