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Simplifying 200 = -16t2 + 150t Reorder the terms: 200 = 150t + -16t2 Solving 200 = 150t + -16t2 Solving for variable 't'. Reorder the terms: 200 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 200 + -150t + 16t2 = 0 + -16t2 + 16t2 200 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 200 + -150t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(100 + -75t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(100 + -75t + 8t2)' equal to zero and attempt to solve: Simplifying 100 + -75t + 8t2 = 0 Solving 100 + -75t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 12.5 + -9.375t + t2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -9.375t + -12.5 + t2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -9.375t + t2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -9.375t + t2 = 0 + -12.5 -9.375t + t2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -9.375t + t2 = -12.5 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 = -12.5 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = -12.5 + 21.97265625 Combine like terms: -12.5 + 21.97265625 = 9.47265625 21.97265625 + -9.375t + t2 = 9.47265625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 9.47265625 Calculate the square root of the right side: 3.077768063 Break this problem into two subproblems by setting (t + -4.6875) equal to 3.077768063 and -3.077768063.Subproblem 1
t + -4.6875 = 3.077768063 Simplifying t + -4.6875 = 3.077768063 Reorder the terms: -4.6875 + t = 3.077768063 Solving -4.6875 + t = 3.077768063 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 = 3.077768063 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 3.077768063 + 4.6875 t = 3.077768063 + 4.6875 Combine like terms: 3.077768063 + 4.6875 = 7.765268063 t = 7.765268063 Simplifying t = 7.765268063Subproblem 2
t + -4.6875 = -3.077768063 Simplifying t + -4.6875 = -3.077768063 Reorder the terms: -4.6875 + t = -3.077768063 Solving -4.6875 + t = -3.077768063 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 = -3.077768063 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -3.077768063 + 4.6875 t = -3.077768063 + 4.6875 Combine like terms: -3.077768063 + 4.6875 = 1.609731937 t = 1.609731937 Simplifying t = 1.609731937Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.765268063, 1.609731937}Solution
t = {7.765268063, 1.609731937}
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