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Simplifying Y2 + 13Y + -64 = 0 Reorder the terms: -64 + 13Y + Y2 = 0 Solving -64 + 13Y + Y2 = 0 Solving for variable 'Y'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 13Y + 64 + Y2 = 0 + 64 Reorder the terms: -64 + 64 + 13Y + Y2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 13Y + Y2 = 0 + 64 13Y + Y2 = 0 + 64 Combine like terms: 0 + 64 = 64 13Y + Y2 = 64 The Y term is 13Y. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13Y + 42.25 + Y2 = 64 + 42.25 Reorder the terms: 42.25 + 13Y + Y2 = 64 + 42.25 Combine like terms: 64 + 42.25 = 106.25 42.25 + 13Y + Y2 = 106.25 Factor a perfect square on the left side: (Y + 6.5)(Y + 6.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (Y + 6.5) equal to 10.307764064 and -10.307764064.Subproblem 1
Y + 6.5 = 10.307764064 Simplifying Y + 6.5 = 10.307764064 Reorder the terms: 6.5 + Y = 10.307764064 Solving 6.5 + Y = 10.307764064 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + Y = 10.307764064 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + Y = 10.307764064 + -6.5 Y = 10.307764064 + -6.5 Combine like terms: 10.307764064 + -6.5 = 3.807764064 Y = 3.807764064 Simplifying Y = 3.807764064Subproblem 2
Y + 6.5 = -10.307764064 Simplifying Y + 6.5 = -10.307764064 Reorder the terms: 6.5 + Y = -10.307764064 Solving 6.5 + Y = -10.307764064 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + Y = -10.307764064 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + Y = -10.307764064 + -6.5 Y = -10.307764064 + -6.5 Combine like terms: -10.307764064 + -6.5 = -16.807764064 Y = -16.807764064 Simplifying Y = -16.807764064Solution
The solution to the problem is based on the solutions from the subproblems. Y = {3.807764064, -16.807764064}
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