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Simplifying 170 = -16t2 + 122t + 131 Reorder the terms: 170 = 131 + 122t + -16t2 Solving 170 = 131 + 122t + -16t2 Solving for variable 't'. Combine like terms: 170 + -131 = 39 39 + -122t + 16t2 = 131 + 122t + -16t2 + -131 + -122t + 16t2 Reorder the terms: 39 + -122t + 16t2 = 131 + -131 + 122t + -122t + -16t2 + 16t2 Combine like terms: 131 + -131 = 0 39 + -122t + 16t2 = 0 + 122t + -122t + -16t2 + 16t2 39 + -122t + 16t2 = 122t + -122t + -16t2 + 16t2 Combine like terms: 122t + -122t = 0 39 + -122t + 16t2 = 0 + -16t2 + 16t2 39 + -122t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 39 + -122t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.4375 + -7.625t + t2 = 0 Move the constant term to the right: Add '-2.4375' to each side of the equation. 2.4375 + -7.625t + -2.4375 + t2 = 0 + -2.4375 Reorder the terms: 2.4375 + -2.4375 + -7.625t + t2 = 0 + -2.4375 Combine like terms: 2.4375 + -2.4375 = 0.0000 0.0000 + -7.625t + t2 = 0 + -2.4375 -7.625t + t2 = 0 + -2.4375 Combine like terms: 0 + -2.4375 = -2.4375 -7.625t + t2 = -2.4375 The t term is -7.625t. Take half its coefficient (-3.8125). Square it (14.53515625) and add it to both sides. Add '14.53515625' to each side of the equation. -7.625t + 14.53515625 + t2 = -2.4375 + 14.53515625 Reorder the terms: 14.53515625 + -7.625t + t2 = -2.4375 + 14.53515625 Combine like terms: -2.4375 + 14.53515625 = 12.09765625 14.53515625 + -7.625t + t2 = 12.09765625 Factor a perfect square on the left side: (t + -3.8125)(t + -3.8125) = 12.09765625 Calculate the square root of the right side: 3.478168519 Break this problem into two subproblems by setting (t + -3.8125) equal to 3.478168519 and -3.478168519.Subproblem 1
t + -3.8125 = 3.478168519 Simplifying t + -3.8125 = 3.478168519 Reorder the terms: -3.8125 + t = 3.478168519 Solving -3.8125 + t = 3.478168519 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + t = 3.478168519 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + t = 3.478168519 + 3.8125 t = 3.478168519 + 3.8125 Combine like terms: 3.478168519 + 3.8125 = 7.290668519 t = 7.290668519 Simplifying t = 7.290668519Subproblem 2
t + -3.8125 = -3.478168519 Simplifying t + -3.8125 = -3.478168519 Reorder the terms: -3.8125 + t = -3.478168519 Solving -3.8125 + t = -3.478168519 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + t = -3.478168519 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + t = -3.478168519 + 3.8125 t = -3.478168519 + 3.8125 Combine like terms: -3.478168519 + 3.8125 = 0.334331481 t = 0.334331481 Simplifying t = 0.334331481Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.290668519, 0.334331481}
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