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Simplifying y2 + 17y = 72 + 0 Reorder the terms: 17y + y2 = 72 + 0 Combine like terms: 72 + 0 = 72 17y + y2 = 72 Solving 17y + y2 = 72 Solving for variable 'y'. Reorder the terms: -72 + 17y + y2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + 17y + y2 = 0 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 = 3.510412149 y = 3.510412149 Simplifying y = 3.510412149Subproblem 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 = -20.510412149 y = -20.510412149 Simplifying y = -20.510412149Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.510412149, -20.510412149}
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