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Simplifying y2 + 18y + -81 = 0 Reorder the terms: -81 + 18y + y2 = 0 Solving -81 + 18y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 18y + 81 + y2 = 0 + 81 Reorder the terms: -81 + 81 + 18y + y2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 18y + y2 = 0 + 81 18y + y2 = 0 + 81 Combine like terms: 0 + 81 = 81 18y + y2 = 81 The y term is 18y. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18y + 81 + y2 = 81 + 81 Reorder the terms: 81 + 18y + y2 = 81 + 81 Combine like terms: 81 + 81 = 162 81 + 18y + y2 = 162 Factor a perfect square on the left side: (y + 9)(y + 9) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (y + 9) equal to 12.727922061 and -12.727922061.Subproblem 1
y + 9 = 12.727922061 Simplifying y + 9 = 12.727922061 Reorder the terms: 9 + y = 12.727922061 Solving 9 + y = 12.727922061 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = 12.727922061 + -9 Combine like terms: 9 + -9 = 0 0 + y = 12.727922061 + -9 y = 12.727922061 + -9 Combine like terms: 12.727922061 + -9 = 3.727922061 y = 3.727922061 Simplifying y = 3.727922061Subproblem 2
y + 9 = -12.727922061 Simplifying y + 9 = -12.727922061 Reorder the terms: 9 + y = -12.727922061 Solving 9 + y = -12.727922061 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = -12.727922061 + -9 Combine like terms: 9 + -9 = 0 0 + y = -12.727922061 + -9 y = -12.727922061 + -9 Combine like terms: -12.727922061 + -9 = -21.727922061 y = -21.727922061 Simplifying y = -21.727922061Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.727922061, -21.727922061}
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