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Simplifying 0 = 3 + -9.8t + -16t2 Solving 0 = 3 + -9.8t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + 9.8t + 16t2 = 3 + -9.8t + -16t2 + -3 + 9.8t + 16t2 Reorder the terms: -3 + 9.8t + 16t2 = 3 + -3 + -9.8t + 9.8t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + 9.8t + 16t2 = 0 + -9.8t + 9.8t + -16t2 + 16t2 -3 + 9.8t + 16t2 = -9.8t + 9.8t + -16t2 + 16t2 Combine like terms: -9.8t + 9.8t = 0.0 -3 + 9.8t + 16t2 = 0.0 + -16t2 + 16t2 -3 + 9.8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + 9.8t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + 0.6125t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 0.6125t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 0.6125t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 0.6125t + t2 = 0 + 0.1875 0.6125t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 0.6125t + t2 = 0.1875 The t term is 0.6125t. Take half its coefficient (0.30625). Square it (0.0937890625) and add it to both sides. Add '0.0937890625' to each side of the equation. 0.6125t + 0.0937890625 + t2 = 0.1875 + 0.0937890625 Reorder the terms: 0.0937890625 + 0.6125t + t2 = 0.1875 + 0.0937890625 Combine like terms: 0.1875 + 0.0937890625 = 0.2812890625 0.0937890625 + 0.6125t + t2 = 0.2812890625 Factor a perfect square on the left side: (t + 0.30625)(t + 0.30625) = 0.2812890625 Calculate the square root of the right side: 0.530366913 Break this problem into two subproblems by setting (t + 0.30625) equal to 0.530366913 and -0.530366913.Subproblem 1
t + 0.30625 = 0.530366913 Simplifying t + 0.30625 = 0.530366913 Reorder the terms: 0.30625 + t = 0.530366913 Solving 0.30625 + t = 0.530366913 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.30625' to each side of the equation. 0.30625 + -0.30625 + t = 0.530366913 + -0.30625 Combine like terms: 0.30625 + -0.30625 = 0.00000 0.00000 + t = 0.530366913 + -0.30625 t = 0.530366913 + -0.30625 Combine like terms: 0.530366913 + -0.30625 = 0.224116913 t = 0.224116913 Simplifying t = 0.224116913Subproblem 2
t + 0.30625 = -0.530366913 Simplifying t + 0.30625 = -0.530366913 Reorder the terms: 0.30625 + t = -0.530366913 Solving 0.30625 + t = -0.530366913 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.30625' to each side of the equation. 0.30625 + -0.30625 + t = -0.530366913 + -0.30625 Combine like terms: 0.30625 + -0.30625 = 0.00000 0.00000 + t = -0.530366913 + -0.30625 t = -0.530366913 + -0.30625 Combine like terms: -0.530366913 + -0.30625 = -0.836616913 t = -0.836616913 Simplifying t = -0.836616913Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.224116913, -0.836616913}
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