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Simplifying (2.5y + 100) * y + 100y = 9800 Reorder the terms: (100 + 2.5y) * y + 100y = 9800 Reorder the terms for easier multiplication: y(100 + 2.5y) + 100y = 9800 (100 * y + 2.5y * y) + 100y = 9800 (100y + 2.5y2) + 100y = 9800 Reorder the terms: 100y + 100y + 2.5y2 = 9800 Combine like terms: 100y + 100y = 200y 200y + 2.5y2 = 9800 Solving 200y + 2.5y2 = 9800 Solving for variable 'y'. Reorder the terms: -9800 + 200y + 2.5y2 = 9800 + -9800 Combine like terms: 9800 + -9800 = 0 -9800 + 200y + 2.5y2 = 0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -3920 + 80y + y2 = 0 Move the constant term to the right: Add '3920' to each side of the equation. -3920 + 80y + 3920 + y2 = 0 + 3920 Reorder the terms: -3920 + 3920 + 80y + y2 = 0 + 3920 Combine like terms: -3920 + 3920 = 0 0 + 80y + y2 = 0 + 3920 80y + y2 = 0 + 3920 Combine like terms: 0 + 3920 = 3920 80y + y2 = 3920 The y term is 80y. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80y + 1600 + y2 = 3920 + 1600 Reorder the terms: 1600 + 80y + y2 = 3920 + 1600 Combine like terms: 3920 + 1600 = 5520 1600 + 80y + y2 = 5520 Factor a perfect square on the left side: (y + 40)(y + 40) = 5520 Calculate the square root of the right side: 74.296702484 Break this problem into two subproblems by setting (y + 40) equal to 74.296702484 and -74.296702484.Subproblem 1
y + 40 = 74.296702484 Simplifying y + 40 = 74.296702484 Reorder the terms: 40 + y = 74.296702484 Solving 40 + y = 74.296702484 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + y = 74.296702484 + -40 Combine like terms: 40 + -40 = 0 0 + y = 74.296702484 + -40 y = 74.296702484 + -40 Combine like terms: 74.296702484 + -40 = 34.296702484 y = 34.296702484 Simplifying y = 34.296702484Subproblem 2
y + 40 = -74.296702484 Simplifying y + 40 = -74.296702484 Reorder the terms: 40 + y = -74.296702484 Solving 40 + y = -74.296702484 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + y = -74.296702484 + -40 Combine like terms: 40 + -40 = 0 0 + y = -74.296702484 + -40 y = -74.296702484 + -40 Combine like terms: -74.296702484 + -40 = -114.296702484 y = -114.296702484 Simplifying y = -114.296702484Solution
The solution to the problem is based on the solutions from the subproblems. y = {34.296702484, -114.296702484}
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