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Simplifying t2 + 18t = 81 Reorder the terms: 18t + t2 = 81 Solving 18t + t2 = 81 Solving for variable 't'. Reorder the terms: -81 + 18t + t2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 18t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 18t + 81 + t2 = 0 + 81 Reorder the terms: -81 + 81 + 18t + t2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 18t + t2 = 0 + 81 18t + t2 = 0 + 81 Combine like terms: 0 + 81 = 81 18t + t2 = 81 The t term is 18t. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18t + 81 + t2 = 81 + 81 Reorder the terms: 81 + 18t + t2 = 81 + 81 Combine like terms: 81 + 81 = 162 81 + 18t + t2 = 162 Factor a perfect square on the left side: (t + 9)(t + 9) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (t + 9) equal to 12.727922061 and -12.727922061.Subproblem 1
t + 9 = 12.727922061 Simplifying t + 9 = 12.727922061 Reorder the terms: 9 + t = 12.727922061 Solving 9 + t = 12.727922061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = 12.727922061 + -9 Combine like terms: 9 + -9 = 0 0 + t = 12.727922061 + -9 t = 12.727922061 + -9 Combine like terms: 12.727922061 + -9 = 3.727922061 t = 3.727922061 Simplifying t = 3.727922061Subproblem 2
t + 9 = -12.727922061 Simplifying t + 9 = -12.727922061 Reorder the terms: 9 + t = -12.727922061 Solving 9 + t = -12.727922061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = -12.727922061 + -9 Combine like terms: 9 + -9 = 0 0 + t = -12.727922061 + -9 t = -12.727922061 + -9 Combine like terms: -12.727922061 + -9 = -21.727922061 t = -21.727922061 Simplifying t = -21.727922061Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.727922061, -21.727922061}
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