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Simplifying 210y + -1y2 = 6000 Solving 210y + -1y2 = 6000 Solving for variable 'y'. Reorder the terms: -6000 + 210y + -1y2 = 6000 + -6000 Combine like terms: 6000 + -6000 = 0 -6000 + 210y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6000 + -210y + y2 = 0 Move the constant term to the right: Add '-6000' to each side of the equation. 6000 + -210y + -6000 + y2 = 0 + -6000 Reorder the terms: 6000 + -6000 + -210y + y2 = 0 + -6000 Combine like terms: 6000 + -6000 = 0 0 + -210y + y2 = 0 + -6000 -210y + y2 = 0 + -6000 Combine like terms: 0 + -6000 = -6000 -210y + y2 = -6000 The y term is -210y. Take half its coefficient (-105). Square it (11025) and add it to both sides. Add '11025' to each side of the equation. -210y + 11025 + y2 = -6000 + 11025 Reorder the terms: 11025 + -210y + y2 = -6000 + 11025 Combine like terms: -6000 + 11025 = 5025 11025 + -210y + y2 = 5025 Factor a perfect square on the left side: (y + -105)(y + -105) = 5025 Calculate the square root of the right side: 70.887234394 Break this problem into two subproblems by setting (y + -105) equal to 70.887234394 and -70.887234394.Subproblem 1
y + -105 = 70.887234394 Simplifying y + -105 = 70.887234394 Reorder the terms: -105 + y = 70.887234394 Solving -105 + y = 70.887234394 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + y = 70.887234394 + 105 Combine like terms: -105 + 105 = 0 0 + y = 70.887234394 + 105 y = 70.887234394 + 105 Combine like terms: 70.887234394 + 105 = 175.887234394 y = 175.887234394 Simplifying y = 175.887234394Subproblem 2
y + -105 = -70.887234394 Simplifying y + -105 = -70.887234394 Reorder the terms: -105 + y = -70.887234394 Solving -105 + y = -70.887234394 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + y = -70.887234394 + 105 Combine like terms: -105 + 105 = 0 0 + y = -70.887234394 + 105 y = -70.887234394 + 105 Combine like terms: -70.887234394 + 105 = 34.112765606 y = 34.112765606 Simplifying y = 34.112765606Solution
The solution to the problem is based on the solutions from the subproblems. y = {175.887234394, 34.112765606}
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