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Simplifying (2y + 9) * y + -2(2y + 9) + -8y = 0 Reorder the terms: (9 + 2y) * y + -2(2y + 9) + -8y = 0 Reorder the terms for easier multiplication: y(9 + 2y) + -2(2y + 9) + -8y = 0 (9 * y + 2y * y) + -2(2y + 9) + -8y = 0 (9y + 2y2) + -2(2y + 9) + -8y = 0 Reorder the terms: 9y + 2y2 + -2(9 + 2y) + -8y = 0 9y + 2y2 + (9 * -2 + 2y * -2) + -8y = 0 9y + 2y2 + (-18 + -4y) + -8y = 0 Reorder the terms: -18 + 9y + -4y + -8y + 2y2 = 0 Combine like terms: 9y + -4y = 5y -18 + 5y + -8y + 2y2 = 0 Combine like terms: 5y + -8y = -3y -18 + -3y + 2y2 = 0 Solving -18 + -3y + 2y2 = 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'. -9 + -1.5y + y2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -1.5y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -1.5y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1.5y + y2 = 0 + 9 -1.5y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1.5y + y2 = 9 The y term is -1.5y. 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. -1.5y + 0.5625 + y2 = 9 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 9 + 0.5625 Combine like terms: 9 + 0.5625 = 9.5625 0.5625 + -1.5y + y2 = 9.5625 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (y + -0.75) equal to 3.092329219 and -3.092329219.Subproblem 1
y + -0.75 = 3.092329219 Simplifying y + -0.75 = 3.092329219 Reorder the terms: -0.75 + y = 3.092329219 Solving -0.75 + y = 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 + y = 3.092329219 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 3.092329219 + 0.75 y = 3.092329219 + 0.75 Combine like terms: 3.092329219 + 0.75 = 3.842329219 y = 3.842329219 Simplifying y = 3.842329219Subproblem 2
y + -0.75 = -3.092329219 Simplifying y + -0.75 = -3.092329219 Reorder the terms: -0.75 + y = -3.092329219 Solving -0.75 + y = -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 + y = -3.092329219 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -3.092329219 + 0.75 y = -3.092329219 + 0.75 Combine like terms: -3.092329219 + 0.75 = -2.342329219 y = -2.342329219 Simplifying y = -2.342329219Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.842329219, -2.342329219}
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