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Simplifying t2 + 18t = -61 Reorder the terms: 18t + t2 = -61 Solving 18t + t2 = -61 Solving for variable 't'. Reorder the terms: 61 + 18t + t2 = -61 + 61 Combine like terms: -61 + 61 = 0 61 + 18t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-61' to each side of the equation. 61 + 18t + -61 + t2 = 0 + -61 Reorder the terms: 61 + -61 + 18t + t2 = 0 + -61 Combine like terms: 61 + -61 = 0 0 + 18t + t2 = 0 + -61 18t + t2 = 0 + -61 Combine like terms: 0 + -61 = -61 18t + t2 = -61 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 = -61 + 81 Reorder the terms: 81 + 18t + t2 = -61 + 81 Combine like terms: -61 + 81 = 20 81 + 18t + t2 = 20 Factor a perfect square on the left side: (t + 9)(t + 9) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (t + 9) equal to 4.472135955 and -4.472135955.Subproblem 1
t + 9 = 4.472135955 Simplifying t + 9 = 4.472135955 Reorder the terms: 9 + t = 4.472135955 Solving 9 + t = 4.472135955 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 = 4.472135955 + -9 Combine like terms: 9 + -9 = 0 0 + t = 4.472135955 + -9 t = 4.472135955 + -9 Combine like terms: 4.472135955 + -9 = -4.527864045 t = -4.527864045 Simplifying t = -4.527864045Subproblem 2
t + 9 = -4.472135955 Simplifying t + 9 = -4.472135955 Reorder the terms: 9 + t = -4.472135955 Solving 9 + t = -4.472135955 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 = -4.472135955 + -9 Combine like terms: 9 + -9 = 0 0 + t = -4.472135955 + -9 t = -4.472135955 + -9 Combine like terms: -4.472135955 + -9 = -13.472135955 t = -13.472135955 Simplifying t = -13.472135955Solution
The solution to the problem is based on the solutions from the subproblems. t = {-4.527864045, -13.472135955}
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