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Simplifying 0 = -16t2 + 125t + 30 Reorder the terms: 0 = 30 + 125t + -16t2 Solving 0 = 30 + 125t + -16t2 Solving for variable 't'. Combine like terms: 0 + -30 = -30 -30 + -125t + 16t2 = 30 + 125t + -16t2 + -30 + -125t + 16t2 Reorder the terms: -30 + -125t + 16t2 = 30 + -30 + 125t + -125t + -16t2 + 16t2 Combine like terms: 30 + -30 = 0 -30 + -125t + 16t2 = 0 + 125t + -125t + -16t2 + 16t2 -30 + -125t + 16t2 = 125t + -125t + -16t2 + 16t2 Combine like terms: 125t + -125t = 0 -30 + -125t + 16t2 = 0 + -16t2 + 16t2 -30 + -125t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -30 + -125t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.875 + -7.8125t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -7.8125t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -7.8125t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -7.8125t + t2 = 0 + 1.875 -7.8125t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -7.8125t + t2 = 1.875 The t term is -7.8125t. Take half its coefficient (-3.90625). Square it (15.25878906) and add it to both sides. Add '15.25878906' to each side of the equation. -7.8125t + 15.25878906 + t2 = 1.875 + 15.25878906 Reorder the terms: 15.25878906 + -7.8125t + t2 = 1.875 + 15.25878906 Combine like terms: 1.875 + 15.25878906 = 17.13378906 15.25878906 + -7.8125t + t2 = 17.13378906 Factor a perfect square on the left side: (t + -3.90625)(t + -3.90625) = 17.13378906 Calculate the square root of the right side: 4.139298136 Break this problem into two subproblems by setting (t + -3.90625) equal to 4.139298136 and -4.139298136.Subproblem 1
t + -3.90625 = 4.139298136 Simplifying t + -3.90625 = 4.139298136 Reorder the terms: -3.90625 + t = 4.139298136 Solving -3.90625 + t = 4.139298136 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + t = 4.139298136 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = 4.139298136 + 3.90625 t = 4.139298136 + 3.90625 Combine like terms: 4.139298136 + 3.90625 = 8.045548136 t = 8.045548136 Simplifying t = 8.045548136Subproblem 2
t + -3.90625 = -4.139298136 Simplifying t + -3.90625 = -4.139298136 Reorder the terms: -3.90625 + t = -4.139298136 Solving -3.90625 + t = -4.139298136 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + t = -4.139298136 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + t = -4.139298136 + 3.90625 t = -4.139298136 + 3.90625 Combine like terms: -4.139298136 + 3.90625 = -0.233048136 t = -0.233048136 Simplifying t = -0.233048136Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.045548136, -0.233048136}
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