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Simplifying 39 = 16t2 + -113t Reorder the terms: 39 = -113t + 16t2 Solving 39 = -113t + 16t2 Solving for variable 't'. Reorder the terms: 39 + 113t + -16t2 = -113t + 113t + 16t2 + -16t2 Combine like terms: -113t + 113t = 0 39 + 113t + -16t2 = 0 + 16t2 + -16t2 39 + 113t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 39 + 113t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.4375 + -7.0625t + t2 = 0 Move the constant term to the right: Add '2.4375' to each side of the equation. -2.4375 + -7.0625t + 2.4375 + t2 = 0 + 2.4375 Reorder the terms: -2.4375 + 2.4375 + -7.0625t + t2 = 0 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + -7.0625t + t2 = 0 + 2.4375 -7.0625t + t2 = 0 + 2.4375 Combine like terms: 0 + 2.4375 = 2.4375 -7.0625t + t2 = 2.4375 The t term is -7.0625t. Take half its coefficient (-3.53125). Square it (12.46972656) and add it to both sides. Add '12.46972656' to each side of the equation. -7.0625t + 12.46972656 + t2 = 2.4375 + 12.46972656 Reorder the terms: 12.46972656 + -7.0625t + t2 = 2.4375 + 12.46972656 Combine like terms: 2.4375 + 12.46972656 = 14.90722656 12.46972656 + -7.0625t + t2 = 14.90722656 Factor a perfect square on the left side: (t + -3.53125)(t + -3.53125) = 14.90722656 Calculate the square root of the right side: 3.86098777 Break this problem into two subproblems by setting (t + -3.53125) equal to 3.86098777 and -3.86098777.Subproblem 1
t + -3.53125 = 3.86098777 Simplifying t + -3.53125 = 3.86098777 Reorder the terms: -3.53125 + t = 3.86098777 Solving -3.53125 + t = 3.86098777 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = 3.86098777 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = 3.86098777 + 3.53125 t = 3.86098777 + 3.53125 Combine like terms: 3.86098777 + 3.53125 = 7.39223777 t = 7.39223777 Simplifying t = 7.39223777Subproblem 2
t + -3.53125 = -3.86098777 Simplifying t + -3.53125 = -3.86098777 Reorder the terms: -3.53125 + t = -3.86098777 Solving -3.53125 + t = -3.86098777 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = -3.86098777 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = -3.86098777 + 3.53125 t = -3.86098777 + 3.53125 Combine like terms: -3.86098777 + 3.53125 = -0.32973777 t = -0.32973777 Simplifying t = -0.32973777Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.39223777, -0.32973777}
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