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Simplifying 9 = (4y4) + (8y2) Reorder the terms: 9 = (8y2) + (4y4) Solving 9 = (8y2) + (4y4) Solving for variable 'y'. Reorder the terms: 9 + (-8y2) + (-4y4) = (8y2) + (-8y2) + (4y4) + (-4y4) Combine like terms: (8y2) + (-8y2) = 0 9 + (-8y2) + (-4y4) = 0 + (4y4) + (-4y4) 9 + (-8y2) + (-4y4) = (4y4) + (-4y4) Combine like terms: (4y4) + (-4y4) = 0 9 + (-8y2) + (-4y4) = 0 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 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 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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