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Simplifying 0 = -16t2 + 150t + 171 Reorder the terms: 0 = 171 + 150t + -16t2 Solving 0 = 171 + 150t + -16t2 Solving for variable 't'. Combine like terms: 0 + -171 = -171 -171 + -150t + 16t2 = 171 + 150t + -16t2 + -171 + -150t + 16t2 Reorder the terms: -171 + -150t + 16t2 = 171 + -171 + 150t + -150t + -16t2 + 16t2 Combine like terms: 171 + -171 = 0 -171 + -150t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -171 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -171 + -150t + 16t2 = 0 + -16t2 + 16t2 -171 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -171 + -150t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -10.6875 + -9.375t + t2 = 0 Move the constant term to the right: Add '10.6875' to each side of the equation. -10.6875 + -9.375t + 10.6875 + t2 = 0 + 10.6875 Reorder the terms: -10.6875 + 10.6875 + -9.375t + t2 = 0 + 10.6875 Combine like terms: -10.6875 + 10.6875 = 0.0000 0.0000 + -9.375t + t2 = 0 + 10.6875 -9.375t + t2 = 0 + 10.6875 Combine like terms: 0 + 10.6875 = 10.6875 -9.375t + t2 = 10.6875 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 = 10.6875 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 10.6875 + 21.97265625 Combine like terms: 10.6875 + 21.97265625 = 32.66015625 21.97265625 + -9.375t + t2 = 32.66015625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 32.66015625 Calculate the square root of the right side: 5.714906495 Break this problem into two subproblems by setting (t + -4.6875) equal to 5.714906495 and -5.714906495.Subproblem 1
t + -4.6875 = 5.714906495 Simplifying t + -4.6875 = 5.714906495 Reorder the terms: -4.6875 + t = 5.714906495 Solving -4.6875 + t = 5.714906495 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 = 5.714906495 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 5.714906495 + 4.6875 t = 5.714906495 + 4.6875 Combine like terms: 5.714906495 + 4.6875 = 10.402406495 t = 10.402406495 Simplifying t = 10.402406495Subproblem 2
t + -4.6875 = -5.714906495 Simplifying t + -4.6875 = -5.714906495 Reorder the terms: -4.6875 + t = -5.714906495 Solving -4.6875 + t = -5.714906495 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 = -5.714906495 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -5.714906495 + 4.6875 t = -5.714906495 + 4.6875 Combine like terms: -5.714906495 + 4.6875 = -1.027406495 t = -1.027406495 Simplifying t = -1.027406495Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.402406495, -1.027406495}
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