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Simplifying 1.8y2 + 180y + -1800 = 0 Reorder the terms: -1800 + 180y + 1.8y2 = 0 Solving -1800 + 180y + 1.8y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 1.8 the coefficient of the squared term: Divide each side by '1.8'. -1000 + 100y + y2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 100y + 1000 + y2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 100y + y2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 100y + y2 = 0 + 1000 100y + y2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 100y + y2 = 1000 The y term is 100y. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100y + 2500 + y2 = 1000 + 2500 Reorder the terms: 2500 + 100y + y2 = 1000 + 2500 Combine like terms: 1000 + 2500 = 3500 2500 + 100y + y2 = 3500 Factor a perfect square on the left side: (y + 50)(y + 50) = 3500 Calculate the square root of the right side: 59.160797831 Break this problem into two subproblems by setting (y + 50) equal to 59.160797831 and -59.160797831.Subproblem 1
y + 50 = 59.160797831 Simplifying y + 50 = 59.160797831 Reorder the terms: 50 + y = 59.160797831 Solving 50 + y = 59.160797831 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + y = 59.160797831 + -50 Combine like terms: 50 + -50 = 0 0 + y = 59.160797831 + -50 y = 59.160797831 + -50 Combine like terms: 59.160797831 + -50 = 9.160797831 y = 9.160797831 Simplifying y = 9.160797831Subproblem 2
y + 50 = -59.160797831 Simplifying y + 50 = -59.160797831 Reorder the terms: 50 + y = -59.160797831 Solving 50 + y = -59.160797831 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + y = -59.160797831 + -50 Combine like terms: 50 + -50 = 0 0 + y = -59.160797831 + -50 y = -59.160797831 + -50 Combine like terms: -59.160797831 + -50 = -109.160797831 y = -109.160797831 Simplifying y = -109.160797831Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.160797831, -109.160797831}
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