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Simplifying 0 = -16t2 + 49.6t + 5 Reorder the terms: 0 = 5 + 49.6t + -16t2 Solving 0 = 5 + 49.6t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -49.6t + 16t2 = 5 + 49.6t + -16t2 + -5 + -49.6t + 16t2 Reorder the terms: -5 + -49.6t + 16t2 = 5 + -5 + 49.6t + -49.6t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -5 + -49.6t + 16t2 = 0 + 49.6t + -49.6t + -16t2 + 16t2 -5 + -49.6t + 16t2 = 49.6t + -49.6t + -16t2 + 16t2 Combine like terms: 49.6t + -49.6t = 0.0 -5 + -49.6t + 16t2 = 0.0 + -16t2 + 16t2 -5 + -49.6t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + -49.6t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -3.1t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -3.1t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -3.1t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -3.1t + t2 = 0 + 0.3125 -3.1t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -3.1t + t2 = 0.3125 The t term is -3.1t. Take half its coefficient (-1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. -3.1t + 2.4025 + t2 = 0.3125 + 2.4025 Reorder the terms: 2.4025 + -3.1t + t2 = 0.3125 + 2.4025 Combine like terms: 0.3125 + 2.4025 = 2.715 2.4025 + -3.1t + t2 = 2.715 Factor a perfect square on the left side: (t + -1.55)(t + -1.55) = 2.715 Calculate the square root of the right side: 1.647725705 Break this problem into two subproblems by setting (t + -1.55) equal to 1.647725705 and -1.647725705.Subproblem 1
t + -1.55 = 1.647725705 Simplifying t + -1.55 = 1.647725705 Reorder the terms: -1.55 + t = 1.647725705 Solving -1.55 + t = 1.647725705 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + t = 1.647725705 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + t = 1.647725705 + 1.55 t = 1.647725705 + 1.55 Combine like terms: 1.647725705 + 1.55 = 3.197725705 t = 3.197725705 Simplifying t = 3.197725705Subproblem 2
t + -1.55 = -1.647725705 Simplifying t + -1.55 = -1.647725705 Reorder the terms: -1.55 + t = -1.647725705 Solving -1.55 + t = -1.647725705 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + t = -1.647725705 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + t = -1.647725705 + 1.55 t = -1.647725705 + 1.55 Combine like terms: -1.647725705 + 1.55 = -0.097725705 t = -0.097725705 Simplifying t = -0.097725705Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.197725705, -0.097725705}
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