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Simplifying 0 = -16t2 + 150t + 629 Reorder the terms: 0 = 629 + 150t + -16t2 Solving 0 = 629 + 150t + -16t2 Solving for variable 't'. Combine like terms: 0 + -629 = -629 -629 + -150t + 16t2 = 629 + 150t + -16t2 + -629 + -150t + 16t2 Reorder the terms: -629 + -150t + 16t2 = 629 + -629 + 150t + -150t + -16t2 + 16t2 Combine like terms: 629 + -629 = 0 -629 + -150t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -629 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -629 + -150t + 16t2 = 0 + -16t2 + 16t2 -629 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -629 + -150t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -39.3125 + -9.375t + t2 = 0 Move the constant term to the right: Add '39.3125' to each side of the equation. -39.3125 + -9.375t + 39.3125 + t2 = 0 + 39.3125 Reorder the terms: -39.3125 + 39.3125 + -9.375t + t2 = 0 + 39.3125 Combine like terms: -39.3125 + 39.3125 = 0.0000 0.0000 + -9.375t + t2 = 0 + 39.3125 -9.375t + t2 = 0 + 39.3125 Combine like terms: 0 + 39.3125 = 39.3125 -9.375t + t2 = 39.3125 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 = 39.3125 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 39.3125 + 21.97265625 Combine like terms: 39.3125 + 21.97265625 = 61.28515625 21.97265625 + -9.375t + t2 = 61.28515625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 61.28515625 Calculate the square root of the right side: 7.828483649 Break this problem into two subproblems by setting (t + -4.6875) equal to 7.828483649 and -7.828483649.Subproblem 1
t + -4.6875 = 7.828483649 Simplifying t + -4.6875 = 7.828483649 Reorder the terms: -4.6875 + t = 7.828483649 Solving -4.6875 + t = 7.828483649 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 = 7.828483649 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 7.828483649 + 4.6875 t = 7.828483649 + 4.6875 Combine like terms: 7.828483649 + 4.6875 = 12.515983649 t = 12.515983649 Simplifying t = 12.515983649Subproblem 2
t + -4.6875 = -7.828483649 Simplifying t + -4.6875 = -7.828483649 Reorder the terms: -4.6875 + t = -7.828483649 Solving -4.6875 + t = -7.828483649 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 = -7.828483649 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -7.828483649 + 4.6875 t = -7.828483649 + 4.6875 Combine like terms: -7.828483649 + 4.6875 = -3.140983649 t = -3.140983649 Simplifying t = -3.140983649Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.515983649, -3.140983649}
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