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Simplifying 100000 + -30000y + y2 = 0 Solving 100000 + -30000y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-100000' to each side of the equation. 100000 + -30000y + -100000 + y2 = 0 + -100000 Reorder the terms: 100000 + -100000 + -30000y + y2 = 0 + -100000 Combine like terms: 100000 + -100000 = 0 0 + -30000y + y2 = 0 + -100000 -30000y + y2 = 0 + -100000 Combine like terms: 0 + -100000 = -100000 -30000y + y2 = -100000 The y term is -30000y. Take half its coefficient (-15000). Square it (225000000) and add it to both sides. Add '225000000' to each side of the equation. -30000y + 225000000 + y2 = -100000 + 225000000 Reorder the terms: 225000000 + -30000y + y2 = -100000 + 225000000 Combine like terms: -100000 + 225000000 = 224900000 225000000 + -30000y + y2 = 224900000 Factor a perfect square on the left side: (y + -15000)(y + -15000) = 224900000 Calculate the square root of the right side: 14996.666296214 Break this problem into two subproblems by setting (y + -15000) equal to 14996.666296214 and -14996.666296214.Subproblem 1
y + -15000 = 14996.666296214 Simplifying y + -15000 = 14996.666296214 Reorder the terms: -15000 + y = 14996.666296214 Solving -15000 + y = 14996.666296214 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '15000' to each side of the equation. -15000 + 15000 + y = 14996.666296214 + 15000 Combine like terms: -15000 + 15000 = 0 0 + y = 14996.666296214 + 15000 y = 14996.666296214 + 15000 Combine like terms: 14996.666296214 + 15000 = 29996.666296214 y = 29996.666296214 Simplifying y = 29996.666296214Subproblem 2
y + -15000 = -14996.666296214 Simplifying y + -15000 = -14996.666296214 Reorder the terms: -15000 + y = -14996.666296214 Solving -15000 + y = -14996.666296214 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '15000' to each side of the equation. -15000 + 15000 + y = -14996.666296214 + 15000 Combine like terms: -15000 + 15000 = 0 0 + y = -14996.666296214 + 15000 y = -14996.666296214 + 15000 Combine like terms: -14996.666296214 + 15000 = 3.333703786 y = 3.333703786 Simplifying y = 3.333703786Solution
The solution to the problem is based on the solutions from the subproblems. y = {29996.666296214, 3.333703786}
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