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Simplifying 0 = 16t2 + 13t + -13 Reorder the terms: 0 = -13 + 13t + 16t2 Solving 0 = -13 + 13t + 16t2 Solving for variable 't'. Combine like terms: 0 + 13 = 13 13 + -13t + -16t2 = -13 + 13t + 16t2 + 13 + -13t + -16t2 Reorder the terms: 13 + -13t + -16t2 = -13 + 13 + 13t + -13t + 16t2 + -16t2 Combine like terms: -13 + 13 = 0 13 + -13t + -16t2 = 0 + 13t + -13t + 16t2 + -16t2 13 + -13t + -16t2 = 13t + -13t + 16t2 + -16t2 Combine like terms: 13t + -13t = 0 13 + -13t + -16t2 = 0 + 16t2 + -16t2 13 + -13t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 13 + -13t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.8125 + 0.8125t + t2 = 0 Move the constant term to the right: Add '0.8125' to each side of the equation. -0.8125 + 0.8125t + 0.8125 + t2 = 0 + 0.8125 Reorder the terms: -0.8125 + 0.8125 + 0.8125t + t2 = 0 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + 0.8125t + t2 = 0 + 0.8125 0.8125t + t2 = 0 + 0.8125 Combine like terms: 0 + 0.8125 = 0.8125 0.8125t + t2 = 0.8125 The t term is 0.8125t. Take half its coefficient (0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. 0.8125t + 0.1650390625 + t2 = 0.8125 + 0.1650390625 Reorder the terms: 0.1650390625 + 0.8125t + t2 = 0.8125 + 0.1650390625 Combine like terms: 0.8125 + 0.1650390625 = 0.9775390625 0.1650390625 + 0.8125t + t2 = 0.9775390625 Factor a perfect square on the left side: (t + 0.40625)(t + 0.40625) = 0.9775390625 Calculate the square root of the right side: 0.988705751 Break this problem into two subproblems by setting (t + 0.40625) equal to 0.988705751 and -0.988705751.Subproblem 1
t + 0.40625 = 0.988705751 Simplifying t + 0.40625 = 0.988705751 Reorder the terms: 0.40625 + t = 0.988705751 Solving 0.40625 + t = 0.988705751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + t = 0.988705751 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + t = 0.988705751 + -0.40625 t = 0.988705751 + -0.40625 Combine like terms: 0.988705751 + -0.40625 = 0.582455751 t = 0.582455751 Simplifying t = 0.582455751Subproblem 2
t + 0.40625 = -0.988705751 Simplifying t + 0.40625 = -0.988705751 Reorder the terms: 0.40625 + t = -0.988705751 Solving 0.40625 + t = -0.988705751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + t = -0.988705751 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + t = -0.988705751 + -0.40625 t = -0.988705751 + -0.40625 Combine like terms: -0.988705751 + -0.40625 = -1.394955751 t = -1.394955751 Simplifying t = -1.394955751Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.582455751, -1.394955751}
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