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Simplifying 16t2 + -55t + -60 = 0 Reorder the terms: -60 + -55t + 16t2 = 0 Solving -60 + -55t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.75 + -3.4375t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -3.4375t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -3.4375t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -3.4375t + t2 = 0 + 3.75 -3.4375t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -3.4375t + t2 = 3.75 The t term is -3.4375t. Take half its coefficient (-1.71875). Square it (2.954101563) and add it to both sides. Add '2.954101563' to each side of the equation. -3.4375t + 2.954101563 + t2 = 3.75 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375t + t2 = 3.75 + 2.954101563 Combine like terms: 3.75 + 2.954101563 = 6.704101563 2.954101563 + -3.4375t + t2 = 6.704101563 Factor a perfect square on the left side: (t + -1.71875)(t + -1.71875) = 6.704101563 Calculate the square root of the right side: 2.589227986 Break this problem into two subproblems by setting (t + -1.71875) equal to 2.589227986 and -2.589227986.Subproblem 1
t + -1.71875 = 2.589227986 Simplifying t + -1.71875 = 2.589227986 Reorder the terms: -1.71875 + t = 2.589227986 Solving -1.71875 + t = 2.589227986 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + t = 2.589227986 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = 2.589227986 + 1.71875 t = 2.589227986 + 1.71875 Combine like terms: 2.589227986 + 1.71875 = 4.307977986 t = 4.307977986 Simplifying t = 4.307977986Subproblem 2
t + -1.71875 = -2.589227986 Simplifying t + -1.71875 = -2.589227986 Reorder the terms: -1.71875 + t = -2.589227986 Solving -1.71875 + t = -2.589227986 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + t = -2.589227986 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = -2.589227986 + 1.71875 t = -2.589227986 + 1.71875 Combine like terms: -2.589227986 + 1.71875 = -0.870477986 t = -0.870477986 Simplifying t = -0.870477986Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.307977986, -0.870477986}
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