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Simplifying t2 + -18t + -72 = 0 Reorder the terms: -72 + -18t + t2 = 0 Solving -72 + -18t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -18t + 72 + t2 = 0 + 72 Reorder the terms: -72 + 72 + -18t + t2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -18t + t2 = 0 + 72 -18t + t2 = 0 + 72 Combine like terms: 0 + 72 = 72 -18t + t2 = 72 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 = 72 + 81 Reorder the terms: 81 + -18t + t2 = 72 + 81 Combine like terms: 72 + 81 = 153 81 + -18t + t2 = 153 Factor a perfect square on the left side: (t + -9)(t + -9) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (t + -9) equal to 12.369316877 and -12.369316877.Subproblem 1
t + -9 = 12.369316877 Simplifying t + -9 = 12.369316877 Reorder the terms: -9 + t = 12.369316877 Solving -9 + t = 12.369316877 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 = 12.369316877 + 9 Combine like terms: -9 + 9 = 0 0 + t = 12.369316877 + 9 t = 12.369316877 + 9 Combine like terms: 12.369316877 + 9 = 21.369316877 t = 21.369316877 Simplifying t = 21.369316877Subproblem 2
t + -9 = -12.369316877 Simplifying t + -9 = -12.369316877 Reorder the terms: -9 + t = -12.369316877 Solving -9 + t = -12.369316877 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 = -12.369316877 + 9 Combine like terms: -9 + 9 = 0 0 + t = -12.369316877 + 9 t = -12.369316877 + 9 Combine like terms: -12.369316877 + 9 = -3.369316877 t = -3.369316877 Simplifying t = -3.369316877Solution
The solution to the problem is based on the solutions from the subproblems. t = {21.369316877, -3.369316877}
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