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Simplifying 0 = -16t2 + 10t + 1255 Reorder the terms: 0 = 1255 + 10t + -16t2 Solving 0 = 1255 + 10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1255 = -1255 -1255 + -10t + 16t2 = 1255 + 10t + -16t2 + -1255 + -10t + 16t2 Reorder the terms: -1255 + -10t + 16t2 = 1255 + -1255 + 10t + -10t + -16t2 + 16t2 Combine like terms: 1255 + -1255 = 0 -1255 + -10t + 16t2 = 0 + 10t + -10t + -16t2 + 16t2 -1255 + -10t + 16t2 = 10t + -10t + -16t2 + 16t2 Combine like terms: 10t + -10t = 0 -1255 + -10t + 16t2 = 0 + -16t2 + 16t2 -1255 + -10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1255 + -10t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -78.4375 + -0.625t + t2 = 0 Move the constant term to the right: Add '78.4375' to each side of the equation. -78.4375 + -0.625t + 78.4375 + t2 = 0 + 78.4375 Reorder the terms: -78.4375 + 78.4375 + -0.625t + t2 = 0 + 78.4375 Combine like terms: -78.4375 + 78.4375 = 0.0000 0.0000 + -0.625t + t2 = 0 + 78.4375 -0.625t + t2 = 0 + 78.4375 Combine like terms: 0 + 78.4375 = 78.4375 -0.625t + t2 = 78.4375 The t term is -0.625t. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625t + 0.09765625 + t2 = 78.4375 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = 78.4375 + 0.09765625 Combine like terms: 78.4375 + 0.09765625 = 78.53515625 0.09765625 + -0.625t + t2 = 78.53515625 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = 78.53515625 Calculate the square root of the right side: 8.862006333 Break this problem into two subproblems by setting (t + -0.3125) equal to 8.862006333 and -8.862006333.Subproblem 1
t + -0.3125 = 8.862006333 Simplifying t + -0.3125 = 8.862006333 Reorder the terms: -0.3125 + t = 8.862006333 Solving -0.3125 + t = 8.862006333 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = 8.862006333 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 8.862006333 + 0.3125 t = 8.862006333 + 0.3125 Combine like terms: 8.862006333 + 0.3125 = 9.174506333 t = 9.174506333 Simplifying t = 9.174506333Subproblem 2
t + -0.3125 = -8.862006333 Simplifying t + -0.3125 = -8.862006333 Reorder the terms: -0.3125 + t = -8.862006333 Solving -0.3125 + t = -8.862006333 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = -8.862006333 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -8.862006333 + 0.3125 t = -8.862006333 + 0.3125 Combine like terms: -8.862006333 + 0.3125 = -8.549506333 t = -8.549506333 Simplifying t = -8.549506333Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.174506333, -8.549506333}
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