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Simplifying y2 + -465y + -14400 = 0 Reorder the terms: -14400 + -465y + y2 = 0 Solving -14400 + -465y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '14400' to each side of the equation. -14400 + -465y + 14400 + y2 = 0 + 14400 Reorder the terms: -14400 + 14400 + -465y + y2 = 0 + 14400 Combine like terms: -14400 + 14400 = 0 0 + -465y + y2 = 0 + 14400 -465y + y2 = 0 + 14400 Combine like terms: 0 + 14400 = 14400 -465y + y2 = 14400 The y term is -465y. Take half its coefficient (-232.5). Square it (54056.25) and add it to both sides. Add '54056.25' to each side of the equation. -465y + 54056.25 + y2 = 14400 + 54056.25 Reorder the terms: 54056.25 + -465y + y2 = 14400 + 54056.25 Combine like terms: 14400 + 54056.25 = 68456.25 54056.25 + -465y + y2 = 68456.25 Factor a perfect square on the left side: (y + -232.5)(y + -232.5) = 68456.25 Calculate the square root of the right side: 261.641453138 Break this problem into two subproblems by setting (y + -232.5) equal to 261.641453138 and -261.641453138.Subproblem 1
y + -232.5 = 261.641453138 Simplifying y + -232.5 = 261.641453138 Reorder the terms: -232.5 + y = 261.641453138 Solving -232.5 + y = 261.641453138 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '232.5' to each side of the equation. -232.5 + 232.5 + y = 261.641453138 + 232.5 Combine like terms: -232.5 + 232.5 = 0.0 0.0 + y = 261.641453138 + 232.5 y = 261.641453138 + 232.5 Combine like terms: 261.641453138 + 232.5 = 494.141453138 y = 494.141453138 Simplifying y = 494.141453138Subproblem 2
y + -232.5 = -261.641453138 Simplifying y + -232.5 = -261.641453138 Reorder the terms: -232.5 + y = -261.641453138 Solving -232.5 + y = -261.641453138 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '232.5' to each side of the equation. -232.5 + 232.5 + y = -261.641453138 + 232.5 Combine like terms: -232.5 + 232.5 = 0.0 0.0 + y = -261.641453138 + 232.5 y = -261.641453138 + 232.5 Combine like terms: -261.641453138 + 232.5 = -29.141453138 y = -29.141453138 Simplifying y = -29.141453138Solution
The solution to the problem is based on the solutions from the subproblems. y = {494.141453138, -29.141453138}
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