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Simplifying Y2 + -17Y + -72 = 0 Reorder the terms: -72 + -17Y + Y2 = 0 Solving -72 + -17Y + Y2 = 0 Solving for variable 'Y'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -17Y + 72 + Y2 = 0 + 72 Reorder the terms: -72 + 72 + -17Y + Y2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -17Y + Y2 = 0 + 72 -17Y + Y2 = 0 + 72 Combine like terms: 0 + 72 = 72 -17Y + Y2 = 72 The Y term is -17Y. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17Y + 72.25 + Y2 = 72 + 72.25 Reorder the terms: 72.25 + -17Y + Y2 = 72 + 72.25 Combine like terms: 72 + 72.25 = 144.25 72.25 + -17Y + Y2 = 144.25 Factor a perfect square on the left side: (Y + -8.5)(Y + -8.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (Y + -8.5) equal to 12.010412149 and -12.010412149.Subproblem 1
Y + -8.5 = 12.010412149 Simplifying Y + -8.5 = 12.010412149 Reorder the terms: -8.5 + Y = 12.010412149 Solving -8.5 + Y = 12.010412149 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + Y = 12.010412149 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + Y = 12.010412149 + 8.5 Y = 12.010412149 + 8.5 Combine like terms: 12.010412149 + 8.5 = 20.510412149 Y = 20.510412149 Simplifying Y = 20.510412149Subproblem 2
Y + -8.5 = -12.010412149 Simplifying Y + -8.5 = -12.010412149 Reorder the terms: -8.5 + Y = -12.010412149 Solving -8.5 + Y = -12.010412149 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + Y = -12.010412149 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + Y = -12.010412149 + 8.5 Y = -12.010412149 + 8.5 Combine like terms: -12.010412149 + 8.5 = -3.510412149 Y = -3.510412149 Simplifying Y = -3.510412149Solution
The solution to the problem is based on the solutions from the subproblems. Y = {20.510412149, -3.510412149}
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