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Simplifying 3000 = -16t2 + 500t + 10 Reorder the terms: 3000 = 10 + 500t + -16t2 Solving 3000 = 10 + 500t + -16t2 Solving for variable 't'. Combine like terms: 3000 + -10 = 2990 2990 + -500t + 16t2 = 10 + 500t + -16t2 + -10 + -500t + 16t2 Reorder the terms: 2990 + -500t + 16t2 = 10 + -10 + 500t + -500t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 2990 + -500t + 16t2 = 0 + 500t + -500t + -16t2 + 16t2 2990 + -500t + 16t2 = 500t + -500t + -16t2 + 16t2 Combine like terms: 500t + -500t = 0 2990 + -500t + 16t2 = 0 + -16t2 + 16t2 2990 + -500t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 2990 + -500t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1495 + -250t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1495 + -250t + 8t2)' equal to zero and attempt to solve: Simplifying 1495 + -250t + 8t2 = 0 Solving 1495 + -250t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 186.875 + -31.25t + t2 = 0 Move the constant term to the right: Add '-186.875' to each side of the equation. 186.875 + -31.25t + -186.875 + t2 = 0 + -186.875 Reorder the terms: 186.875 + -186.875 + -31.25t + t2 = 0 + -186.875 Combine like terms: 186.875 + -186.875 = 0.000 0.000 + -31.25t + t2 = 0 + -186.875 -31.25t + t2 = 0 + -186.875 Combine like terms: 0 + -186.875 = -186.875 -31.25t + t2 = -186.875 The t term is -31.25t. Take half its coefficient (-15.625). Square it (244.140625) and add it to both sides. Add '244.140625' to each side of the equation. -31.25t + 244.140625 + t2 = -186.875 + 244.140625 Reorder the terms: 244.140625 + -31.25t + t2 = -186.875 + 244.140625 Combine like terms: -186.875 + 244.140625 = 57.265625 244.140625 + -31.25t + t2 = 57.265625 Factor a perfect square on the left side: (t + -15.625)(t + -15.625) = 57.265625 Calculate the square root of the right side: 7.567405434 Break this problem into two subproblems by setting (t + -15.625) equal to 7.567405434 and -7.567405434.Subproblem 1
t + -15.625 = 7.567405434 Simplifying t + -15.625 = 7.567405434 Reorder the terms: -15.625 + t = 7.567405434 Solving -15.625 + t = 7.567405434 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + t = 7.567405434 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + t = 7.567405434 + 15.625 t = 7.567405434 + 15.625 Combine like terms: 7.567405434 + 15.625 = 23.192405434 t = 23.192405434 Simplifying t = 23.192405434Subproblem 2
t + -15.625 = -7.567405434 Simplifying t + -15.625 = -7.567405434 Reorder the terms: -15.625 + t = -7.567405434 Solving -15.625 + t = -7.567405434 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + t = -7.567405434 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + t = -7.567405434 + 15.625 t = -7.567405434 + 15.625 Combine like terms: -7.567405434 + 15.625 = 8.057594566 t = 8.057594566 Simplifying t = 8.057594566Solution
The solution to the problem is based on the solutions from the subproblems. t = {23.192405434, 8.057594566}Solution
t = {23.192405434, 8.057594566}
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