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Simplifying 3 = -16t2 + 150t + 16 Reorder the terms: 3 = 16 + 150t + -16t2 Solving 3 = 16 + 150t + -16t2 Solving for variable 't'. Combine like terms: 3 + -16 = -13 -13 + -150t + 16t2 = 16 + 150t + -16t2 + -16 + -150t + 16t2 Reorder the terms: -13 + -150t + 16t2 = 16 + -16 + 150t + -150t + -16t2 + 16t2 Combine like terms: 16 + -16 = 0 -13 + -150t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -13 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -13 + -150t + 16t2 = 0 + -16t2 + 16t2 -13 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -13 + -150t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.8125 + -9.375t + t2 = 0 Move the constant term to the right: Add '0.8125' to each side of the equation. -0.8125 + -9.375t + 0.8125 + t2 = 0 + 0.8125 Reorder the terms: -0.8125 + 0.8125 + -9.375t + t2 = 0 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + -9.375t + t2 = 0 + 0.8125 -9.375t + t2 = 0 + 0.8125 Combine like terms: 0 + 0.8125 = 0.8125 -9.375t + t2 = 0.8125 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 = 0.8125 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 0.8125 + 21.97265625 Combine like terms: 0.8125 + 21.97265625 = 22.78515625 21.97265625 + -9.375t + t2 = 22.78515625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 22.78515625 Calculate the square root of the right side: 4.773379961 Break this problem into two subproblems by setting (t + -4.6875) equal to 4.773379961 and -4.773379961.Subproblem 1
t + -4.6875 = 4.773379961 Simplifying t + -4.6875 = 4.773379961 Reorder the terms: -4.6875 + t = 4.773379961 Solving -4.6875 + t = 4.773379961 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 = 4.773379961 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 4.773379961 + 4.6875 t = 4.773379961 + 4.6875 Combine like terms: 4.773379961 + 4.6875 = 9.460879961 t = 9.460879961 Simplifying t = 9.460879961Subproblem 2
t + -4.6875 = -4.773379961 Simplifying t + -4.6875 = -4.773379961 Reorder the terms: -4.6875 + t = -4.773379961 Solving -4.6875 + t = -4.773379961 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 = -4.773379961 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -4.773379961 + 4.6875 t = -4.773379961 + 4.6875 Combine like terms: -4.773379961 + 4.6875 = -0.085879961 t = -0.085879961 Simplifying t = -0.085879961Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.460879961, -0.085879961}
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