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Simplifying 1.8y2 + 144y + -1800 = 0 Reorder the terms: -1800 + 144y + 1.8y2 = 0 Solving -1800 + 144y + 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 + 80y + y2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 80y + 1000 + y2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 80y + y2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 80y + y2 = 0 + 1000 80y + y2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 80y + y2 = 1000 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 = 1000 + 1600 Reorder the terms: 1600 + 80y + y2 = 1000 + 1600 Combine like terms: 1000 + 1600 = 2600 1600 + 80y + y2 = 2600 Factor a perfect square on the left side: (y + 40)(y + 40) = 2600 Calculate the square root of the right side: 50.990195136 Break this problem into two subproblems by setting (y + 40) equal to 50.990195136 and -50.990195136.Subproblem 1
y + 40 = 50.990195136 Simplifying y + 40 = 50.990195136 Reorder the terms: 40 + y = 50.990195136 Solving 40 + y = 50.990195136 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 = 50.990195136 + -40 Combine like terms: 40 + -40 = 0 0 + y = 50.990195136 + -40 y = 50.990195136 + -40 Combine like terms: 50.990195136 + -40 = 10.990195136 y = 10.990195136 Simplifying y = 10.990195136Subproblem 2
y + 40 = -50.990195136 Simplifying y + 40 = -50.990195136 Reorder the terms: 40 + y = -50.990195136 Solving 40 + y = -50.990195136 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 = -50.990195136 + -40 Combine like terms: 40 + -40 = 0 0 + y = -50.990195136 + -40 y = -50.990195136 + -40 Combine like terms: -50.990195136 + -40 = -90.990195136 y = -90.990195136 Simplifying y = -90.990195136Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.990195136, -90.990195136}
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