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Simplifying 0 = -16t2 + 38.8t + 3 Reorder the terms: 0 = 3 + 38.8t + -16t2 Solving 0 = 3 + 38.8t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -38.8t + 16t2 = 3 + 38.8t + -16t2 + -3 + -38.8t + 16t2 Reorder the terms: -3 + -38.8t + 16t2 = 3 + -3 + 38.8t + -38.8t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -38.8t + 16t2 = 0 + 38.8t + -38.8t + -16t2 + 16t2 -3 + -38.8t + 16t2 = 38.8t + -38.8t + -16t2 + 16t2 Combine like terms: 38.8t + -38.8t = 0.0 -3 + -38.8t + 16t2 = 0.0 + -16t2 + 16t2 -3 + -38.8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -38.8t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -2.425t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -2.425t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -2.425t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -2.425t + t2 = 0 + 0.1875 -2.425t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -2.425t + t2 = 0.1875 The t term is -2.425t. Take half its coefficient (-1.2125). Square it (1.47015625) and add it to both sides. Add '1.47015625' to each side of the equation. -2.425t + 1.47015625 + t2 = 0.1875 + 1.47015625 Reorder the terms: 1.47015625 + -2.425t + t2 = 0.1875 + 1.47015625 Combine like terms: 0.1875 + 1.47015625 = 1.65765625 1.47015625 + -2.425t + t2 = 1.65765625 Factor a perfect square on the left side: (t + -1.2125)(t + -1.2125) = 1.65765625 Calculate the square root of the right side: 1.2875 Break this problem into two subproblems by setting (t + -1.2125) equal to 1.2875 and -1.2875.Subproblem 1
t + -1.2125 = 1.2875 Simplifying t + -1.2125 = 1.2875 Reorder the terms: -1.2125 + t = 1.2875 Solving -1.2125 + t = 1.2875 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2125' to each side of the equation. -1.2125 + 1.2125 + t = 1.2875 + 1.2125 Combine like terms: -1.2125 + 1.2125 = 0.0000 0.0000 + t = 1.2875 + 1.2125 t = 1.2875 + 1.2125 Combine like terms: 1.2875 + 1.2125 = 2.5 t = 2.5 Simplifying t = 2.5Subproblem 2
t + -1.2125 = -1.2875 Simplifying t + -1.2125 = -1.2875 Reorder the terms: -1.2125 + t = -1.2875 Solving -1.2125 + t = -1.2875 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2125' to each side of the equation. -1.2125 + 1.2125 + t = -1.2875 + 1.2125 Combine like terms: -1.2125 + 1.2125 = 0.0000 0.0000 + t = -1.2875 + 1.2125 t = -1.2875 + 1.2125 Combine like terms: -1.2875 + 1.2125 = -0.075 t = -0.075 Simplifying t = -0.075Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.5, -0.075}
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