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Simplifying t2 + -18t + -80 = 0 Reorder the terms: -80 + -18t + t2 = 0 Solving -80 + -18t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -18t + 80 + t2 = 0 + 80 Reorder the terms: -80 + 80 + -18t + t2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -18t + t2 = 0 + 80 -18t + t2 = 0 + 80 Combine like terms: 0 + 80 = 80 -18t + t2 = 80 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 = 80 + 81 Reorder the terms: 81 + -18t + t2 = 80 + 81 Combine like terms: 80 + 81 = 161 81 + -18t + t2 = 161 Factor a perfect square on the left side: (t + -9)(t + -9) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (t + -9) equal to 12.68857754 and -12.68857754.Subproblem 1
t + -9 = 12.68857754 Simplifying t + -9 = 12.68857754 Reorder the terms: -9 + t = 12.68857754 Solving -9 + t = 12.68857754 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 = 12.68857754 + 9 Combine like terms: -9 + 9 = 0 0 + t = 12.68857754 + 9 t = 12.68857754 + 9 Combine like terms: 12.68857754 + 9 = 21.68857754 t = 21.68857754 Simplifying t = 21.68857754Subproblem 2
t + -9 = -12.68857754 Simplifying t + -9 = -12.68857754 Reorder the terms: -9 + t = -12.68857754 Solving -9 + t = -12.68857754 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 = -12.68857754 + 9 Combine like terms: -9 + 9 = 0 0 + t = -12.68857754 + 9 t = -12.68857754 + 9 Combine like terms: -12.68857754 + 9 = -3.68857754 t = -3.68857754 Simplifying t = -3.68857754Solution
The solution to the problem is based on the solutions from the subproblems. t = {21.68857754, -3.68857754}
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