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Simplifying Y2 + -19Y + 66 = 0 Reorder the terms: 66 + -19Y + Y2 = 0 Solving 66 + -19Y + Y2 = 0 Solving for variable 'Y'. Begin completing the square. Move the constant term to the right: Add '-66' to each side of the equation. 66 + -19Y + -66 + Y2 = 0 + -66 Reorder the terms: 66 + -66 + -19Y + Y2 = 0 + -66 Combine like terms: 66 + -66 = 0 0 + -19Y + Y2 = 0 + -66 -19Y + Y2 = 0 + -66 Combine like terms: 0 + -66 = -66 -19Y + Y2 = -66 The Y term is -19Y. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19Y + 90.25 + Y2 = -66 + 90.25 Reorder the terms: 90.25 + -19Y + Y2 = -66 + 90.25 Combine like terms: -66 + 90.25 = 24.25 90.25 + -19Y + Y2 = 24.25 Factor a perfect square on the left side: (Y + -9.5)(Y + -9.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (Y + -9.5) equal to 4.924428901 and -4.924428901.Subproblem 1
Y + -9.5 = 4.924428901 Simplifying Y + -9.5 = 4.924428901 Reorder the terms: -9.5 + Y = 4.924428901 Solving -9.5 + Y = 4.924428901 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + Y = 4.924428901 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + Y = 4.924428901 + 9.5 Y = 4.924428901 + 9.5 Combine like terms: 4.924428901 + 9.5 = 14.424428901 Y = 14.424428901 Simplifying Y = 14.424428901Subproblem 2
Y + -9.5 = -4.924428901 Simplifying Y + -9.5 = -4.924428901 Reorder the terms: -9.5 + Y = -4.924428901 Solving -9.5 + Y = -4.924428901 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + Y = -4.924428901 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + Y = -4.924428901 + 9.5 Y = -4.924428901 + 9.5 Combine like terms: -4.924428901 + 9.5 = 4.575571099 Y = 4.575571099 Simplifying Y = 4.575571099Solution
The solution to the problem is based on the solutions from the subproblems. Y = {14.424428901, 4.575571099}
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