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Simplifying 1800 = 120y + -1y2 Solving 1800 = 120y + -1y2 Solving for variable 'y'. Reorder the terms: 1800 + -120y + y2 = 120y + -120y + -1y2 + y2 Combine like terms: 120y + -120y = 0 1800 + -120y + y2 = 0 + -1y2 + y2 1800 + -120y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 1800 + -120y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-1800' to each side of the equation. 1800 + -120y + -1800 + y2 = 0 + -1800 Reorder the terms: 1800 + -1800 + -120y + y2 = 0 + -1800 Combine like terms: 1800 + -1800 = 0 0 + -120y + y2 = 0 + -1800 -120y + y2 = 0 + -1800 Combine like terms: 0 + -1800 = -1800 -120y + y2 = -1800 The y term is -120y. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120y + 3600 + y2 = -1800 + 3600 Reorder the terms: 3600 + -120y + y2 = -1800 + 3600 Combine like terms: -1800 + 3600 = 1800 3600 + -120y + y2 = 1800 Factor a perfect square on the left side: (y + -60)(y + -60) = 1800 Calculate the square root of the right side: 42.426406871 Break this problem into two subproblems by setting (y + -60) equal to 42.426406871 and -42.426406871.Subproblem 1
y + -60 = 42.426406871 Simplifying y + -60 = 42.426406871 Reorder the terms: -60 + y = 42.426406871 Solving -60 + y = 42.426406871 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + y = 42.426406871 + 60 Combine like terms: -60 + 60 = 0 0 + y = 42.426406871 + 60 y = 42.426406871 + 60 Combine like terms: 42.426406871 + 60 = 102.426406871 y = 102.426406871 Simplifying y = 102.426406871Subproblem 2
y + -60 = -42.426406871 Simplifying y + -60 = -42.426406871 Reorder the terms: -60 + y = -42.426406871 Solving -60 + y = -42.426406871 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + y = -42.426406871 + 60 Combine like terms: -60 + 60 = 0 0 + y = -42.426406871 + 60 y = -42.426406871 + 60 Combine like terms: -42.426406871 + 60 = 17.573593129 y = 17.573593129 Simplifying y = 17.573593129Solution
The solution to the problem is based on the solutions from the subproblems. y = {102.426406871, 17.573593129}
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