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Simplifying 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 = 10.03222656 12.46972656 + -7.0625t + t2 = 10.03222656 Factor a perfect square on the left side: (t + -3.53125)(t + -3.53125) = 10.03222656 Calculate the square root of the right side: 3.167369028 Break this problem into two subproblems by setting (t + -3.53125) equal to 3.167369028 and -3.167369028.Subproblem 1
t + -3.53125 = 3.167369028 Simplifying t + -3.53125 = 3.167369028 Reorder the terms: -3.53125 + t = 3.167369028 Solving -3.53125 + t = 3.167369028 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 = 3.167369028 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = 3.167369028 + 3.53125 t = 3.167369028 + 3.53125 Combine like terms: 3.167369028 + 3.53125 = 6.698619028 t = 6.698619028 Simplifying t = 6.698619028Subproblem 2
t + -3.53125 = -3.167369028 Simplifying t + -3.53125 = -3.167369028 Reorder the terms: -3.53125 + t = -3.167369028 Solving -3.53125 + t = -3.167369028 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 = -3.167369028 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = -3.167369028 + 3.53125 t = -3.167369028 + 3.53125 Combine like terms: -3.167369028 + 3.53125 = 0.363880972 t = 0.363880972 Simplifying t = 0.363880972Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.698619028, 0.363880972}
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