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Simplifying 0 = -16t2 + 150t + 45 Reorder the terms: 0 = 45 + 150t + -16t2 Solving 0 = 45 + 150t + -16t2 Solving for variable 't'. Combine like terms: 0 + -45 = -45 -45 + -150t + 16t2 = 45 + 150t + -16t2 + -45 + -150t + 16t2 Reorder the terms: -45 + -150t + 16t2 = 45 + -45 + 150t + -150t + -16t2 + 16t2 Combine like terms: 45 + -45 = 0 -45 + -150t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -45 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -45 + -150t + 16t2 = 0 + -16t2 + 16t2 -45 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -45 + -150t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.8125 + -9.375t + t2 = 0 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + -9.375t + 2.8125 + t2 = 0 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + -9.375t + t2 = 0 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + -9.375t + t2 = 0 + 2.8125 -9.375t + t2 = 0 + 2.8125 Combine like terms: 0 + 2.8125 = 2.8125 -9.375t + t2 = 2.8125 The t term is -9.375t. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375t + 21.97265625 + t2 = 2.8125 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 2.8125 + 21.97265625 Combine like terms: 2.8125 + 21.97265625 = 24.78515625 21.97265625 + -9.375t + t2 = 24.78515625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 24.78515625 Calculate the square root of the right side: 4.978469268 Break this problem into two subproblems by setting (t + -4.6875) equal to 4.978469268 and -4.978469268.Subproblem 1
t + -4.6875 = 4.978469268 Simplifying t + -4.6875 = 4.978469268 Reorder the terms: -4.6875 + t = 4.978469268 Solving -4.6875 + t = 4.978469268 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = 4.978469268 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 4.978469268 + 4.6875 t = 4.978469268 + 4.6875 Combine like terms: 4.978469268 + 4.6875 = 9.665969268 t = 9.665969268 Simplifying t = 9.665969268Subproblem 2
t + -4.6875 = -4.978469268 Simplifying t + -4.6875 = -4.978469268 Reorder the terms: -4.6875 + t = -4.978469268 Solving -4.6875 + t = -4.978469268 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = -4.978469268 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -4.978469268 + 4.6875 t = -4.978469268 + 4.6875 Combine like terms: -4.978469268 + 4.6875 = -0.290969268 t = -0.290969268 Simplifying t = -0.290969268Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.665969268, -0.290969268}
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