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Simplifying 0 = -16t2 + 13t + 60 Reorder the terms: 0 = 60 + 13t + -16t2 Solving 0 = 60 + 13t + -16t2 Solving for variable 't'. Combine like terms: 0 + -60 = -60 -60 + -13t + 16t2 = 60 + 13t + -16t2 + -60 + -13t + 16t2 Reorder the terms: -60 + -13t + 16t2 = 60 + -60 + 13t + -13t + -16t2 + 16t2 Combine like terms: 60 + -60 = 0 -60 + -13t + 16t2 = 0 + 13t + -13t + -16t2 + 16t2 -60 + -13t + 16t2 = 13t + -13t + -16t2 + 16t2 Combine like terms: 13t + -13t = 0 -60 + -13t + 16t2 = 0 + -16t2 + 16t2 -60 + -13t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -60 + -13t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.75 + -0.8125t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -0.8125t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -0.8125t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -0.8125t + t2 = 0 + 3.75 -0.8125t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -0.8125t + t2 = 3.75 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 = 3.75 + 0.1650390625 Reorder the terms: 0.1650390625 + -0.8125t + t2 = 3.75 + 0.1650390625 Combine like terms: 3.75 + 0.1650390625 = 3.9150390625 0.1650390625 + -0.8125t + t2 = 3.9150390625 Factor a perfect square on the left side: (t + -0.40625)(t + -0.40625) = 3.9150390625 Calculate the square root of the right side: 1.978645765 Break this problem into two subproblems by setting (t + -0.40625) equal to 1.978645765 and -1.978645765.Subproblem 1
t + -0.40625 = 1.978645765 Simplifying t + -0.40625 = 1.978645765 Reorder the terms: -0.40625 + t = 1.978645765 Solving -0.40625 + t = 1.978645765 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 = 1.978645765 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + t = 1.978645765 + 0.40625 t = 1.978645765 + 0.40625 Combine like terms: 1.978645765 + 0.40625 = 2.384895765 t = 2.384895765 Simplifying t = 2.384895765Subproblem 2
t + -0.40625 = -1.978645765 Simplifying t + -0.40625 = -1.978645765 Reorder the terms: -0.40625 + t = -1.978645765 Solving -0.40625 + t = -1.978645765 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 = -1.978645765 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + t = -1.978645765 + 0.40625 t = -1.978645765 + 0.40625 Combine like terms: -1.978645765 + 0.40625 = -1.572395765 t = -1.572395765 Simplifying t = -1.572395765Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.384895765, -1.572395765}
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