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Simplifying y2 + -6y + -263 = 0 Reorder the terms: -263 + -6y + y2 = 0 Solving -263 + -6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '263' to each side of the equation. -263 + -6y + 263 + y2 = 0 + 263 Reorder the terms: -263 + 263 + -6y + y2 = 0 + 263 Combine like terms: -263 + 263 = 0 0 + -6y + y2 = 0 + 263 -6y + y2 = 0 + 263 Combine like terms: 0 + 263 = 263 -6y + y2 = 263 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 263 + 9 Reorder the terms: 9 + -6y + y2 = 263 + 9 Combine like terms: 263 + 9 = 272 9 + -6y + y2 = 272 Factor a perfect square on the left side: (y + -3)(y + -3) = 272 Calculate the square root of the right side: 16.492422502 Break this problem into two subproblems by setting (y + -3) equal to 16.492422502 and -16.492422502.Subproblem 1
y + -3 = 16.492422502 Simplifying y + -3 = 16.492422502 Reorder the terms: -3 + y = 16.492422502 Solving -3 + y = 16.492422502 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 16.492422502 + 3 Combine like terms: -3 + 3 = 0 0 + y = 16.492422502 + 3 y = 16.492422502 + 3 Combine like terms: 16.492422502 + 3 = 19.492422502 y = 19.492422502 Simplifying y = 19.492422502Subproblem 2
y + -3 = -16.492422502 Simplifying y + -3 = -16.492422502 Reorder the terms: -3 + y = -16.492422502 Solving -3 + y = -16.492422502 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -16.492422502 + 3 Combine like terms: -3 + 3 = 0 0 + y = -16.492422502 + 3 y = -16.492422502 + 3 Combine like terms: -16.492422502 + 3 = -13.492422502 y = -13.492422502 Simplifying y = -13.492422502Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.492422502, -13.492422502}
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