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Simplifying -2y2 + 240y = 4400 Reorder the terms: 240y + -2y2 = 4400 Solving 240y + -2y2 = 4400 Solving for variable 'y'. Reorder the terms: -4400 + 240y + -2y2 = 4400 + -4400 Combine like terms: 4400 + -4400 = 0 -4400 + 240y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2200 + 120y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2200 + 120y + -1y2)' equal to zero and attempt to solve: Simplifying -2200 + 120y + -1y2 = 0 Solving -2200 + 120y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2200 + -120y + y2 = 0 Move the constant term to the right: Add '-2200' to each side of the equation. 2200 + -120y + -2200 + y2 = 0 + -2200 Reorder the terms: 2200 + -2200 + -120y + y2 = 0 + -2200 Combine like terms: 2200 + -2200 = 0 0 + -120y + y2 = 0 + -2200 -120y + y2 = 0 + -2200 Combine like terms: 0 + -2200 = -2200 -120y + y2 = -2200 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 = -2200 + 3600 Reorder the terms: 3600 + -120y + y2 = -2200 + 3600 Combine like terms: -2200 + 3600 = 1400 3600 + -120y + y2 = 1400 Factor a perfect square on the left side: (y + -60)(y + -60) = 1400 Calculate the square root of the right side: 37.416573868 Break this problem into two subproblems by setting (y + -60) equal to 37.416573868 and -37.416573868.Subproblem 1
y + -60 = 37.416573868 Simplifying y + -60 = 37.416573868 Reorder the terms: -60 + y = 37.416573868 Solving -60 + y = 37.416573868 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 = 37.416573868 + 60 Combine like terms: -60 + 60 = 0 0 + y = 37.416573868 + 60 y = 37.416573868 + 60 Combine like terms: 37.416573868 + 60 = 97.416573868 y = 97.416573868 Simplifying y = 97.416573868Subproblem 2
y + -60 = -37.416573868 Simplifying y + -60 = -37.416573868 Reorder the terms: -60 + y = -37.416573868 Solving -60 + y = -37.416573868 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 = -37.416573868 + 60 Combine like terms: -60 + 60 = 0 0 + y = -37.416573868 + 60 y = -37.416573868 + 60 Combine like terms: -37.416573868 + 60 = 22.583426132 y = 22.583426132 Simplifying y = 22.583426132Solution
The solution to the problem is based on the solutions from the subproblems. y = {97.416573868, 22.583426132}Solution
y = {97.416573868, 22.583426132}
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