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Simplifying 0 = -16t2 + 28t + 5 Reorder the terms: 0 = 5 + 28t + -16t2 Solving 0 = 5 + 28t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -28t + 16t2 = 5 + 28t + -16t2 + -5 + -28t + 16t2 Reorder the terms: -5 + -28t + 16t2 = 5 + -5 + 28t + -28t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -5 + -28t + 16t2 = 0 + 28t + -28t + -16t2 + 16t2 -5 + -28t + 16t2 = 28t + -28t + -16t2 + 16t2 Combine like terms: 28t + -28t = 0 -5 + -28t + 16t2 = 0 + -16t2 + 16t2 -5 + -28t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + -28t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -1.75t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -1.75t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -1.75t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -1.75t + t2 = 0 + 0.3125 -1.75t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -1.75t + t2 = 0.3125 The t term is -1.75t. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75t + 0.765625 + t2 = 0.3125 + 0.765625 Reorder the terms: 0.765625 + -1.75t + t2 = 0.3125 + 0.765625 Combine like terms: 0.3125 + 0.765625 = 1.078125 0.765625 + -1.75t + t2 = 1.078125 Factor a perfect square on the left side: (t + -0.875)(t + -0.875) = 1.078125 Calculate the square root of the right side: 1.038327983 Break this problem into two subproblems by setting (t + -0.875) equal to 1.038327983 and -1.038327983.Subproblem 1
t + -0.875 = 1.038327983 Simplifying t + -0.875 = 1.038327983 Reorder the terms: -0.875 + t = 1.038327983 Solving -0.875 + t = 1.038327983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = 1.038327983 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = 1.038327983 + 0.875 t = 1.038327983 + 0.875 Combine like terms: 1.038327983 + 0.875 = 1.913327983 t = 1.913327983 Simplifying t = 1.913327983Subproblem 2
t + -0.875 = -1.038327983 Simplifying t + -0.875 = -1.038327983 Reorder the terms: -0.875 + t = -1.038327983 Solving -0.875 + t = -1.038327983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = -1.038327983 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = -1.038327983 + 0.875 t = -1.038327983 + 0.875 Combine like terms: -1.038327983 + 0.875 = -0.163327983 t = -0.163327983 Simplifying t = -0.163327983Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.913327983, -0.163327983}
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