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Simplifying 2y2(y2 + 2) = y2 + 18 Reorder the terms: 2y2(2 + y2) = y2 + 18 (2 * 2y2 + y2 * 2y2) = y2 + 18 (4y2 + 2y4) = y2 + 18 Reorder the terms: 4y2 + 2y4 = 18 + y2 Solving 4y2 + 2y4 = 18 + y2 Solving for variable 'y'. Reorder the terms: -18 + 4y2 + -1y2 + 2y4 = 18 + y2 + -18 + -1y2 Combine like terms: 4y2 + -1y2 = 3y2 -18 + 3y2 + 2y4 = 18 + y2 + -18 + -1y2 Reorder the terms: -18 + 3y2 + 2y4 = 18 + -18 + y2 + -1y2 Combine like terms: 18 + -18 = 0 -18 + 3y2 + 2y4 = 0 + y2 + -1y2 -18 + 3y2 + 2y4 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -18 + 3y2 + 2y4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + 1.5y2 + y4 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 1.5y2 + 9 + y4 = 0 + 9 Reorder the terms: -9 + 9 + 1.5y2 + y4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 1.5y2 + y4 = 0 + 9 1.5y2 + y4 = 0 + 9 Combine like terms: 0 + 9 = 9 1.5y2 + y4 = 9 The y term is 1.5y2. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5y2 + 0.5625 + y4 = 9 + 0.5625 Reorder the terms: 0.5625 + 1.5y2 + y4 = 9 + 0.5625 Combine like terms: 9 + 0.5625 = 9.5625 0.5625 + 1.5y2 + y4 = 9.5625 Factor a perfect square on the left side: (y2 + 0.75)(y2 + 0.75) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (y2 + 0.75) equal to 3.092329219 and -3.092329219.Subproblem 1
y2 + 0.75 = 3.092329219 Simplifying y2 + 0.75 = 3.092329219 Reorder the terms: 0.75 + y2 = 3.092329219 Solving 0.75 + y2 = 3.092329219 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y2 = 3.092329219 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y2 = 3.092329219 + -0.75 y2 = 3.092329219 + -0.75 Combine like terms: 3.092329219 + -0.75 = 2.342329219 y2 = 2.342329219 Simplifying y2 = 2.342329219 Take the square root of each side: y = {-1.530466994, 1.530466994}Subproblem 2
y2 + 0.75 = -3.092329219 Simplifying y2 + 0.75 = -3.092329219 Reorder the terms: 0.75 + y2 = -3.092329219 Solving 0.75 + y2 = -3.092329219 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y2 = -3.092329219 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y2 = -3.092329219 + -0.75 y2 = -3.092329219 + -0.75 Combine like terms: -3.092329219 + -0.75 = -3.842329219 y2 = -3.842329219 Simplifying y2 = -3.842329219 Reorder the terms: 3.842329219 + y2 = -3.842329219 + 3.842329219 Combine like terms: -3.842329219 + 3.842329219 = 0.000000000 3.842329219 + 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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