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Simplifying -16t2 + 120t + 5 = 50 Reorder the terms: 5 + 120t + -16t2 = 50 Solving 5 + 120t + -16t2 = 50 Solving for variable 't'. Reorder the terms: 5 + -50 + 120t + -16t2 = 50 + -50 Combine like terms: 5 + -50 = -45 -45 + 120t + -16t2 = 50 + -50 Combine like terms: 50 + -50 = 0 -45 + 120t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 2.8125 + -7.5t + t2 = 0 Move the constant term to the right: Add '-2.8125' to each side of the equation. 2.8125 + -7.5t + -2.8125 + t2 = 0 + -2.8125 Reorder the terms: 2.8125 + -2.8125 + -7.5t + t2 = 0 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + -7.5t + t2 = 0 + -2.8125 -7.5t + t2 = 0 + -2.8125 Combine like terms: 0 + -2.8125 = -2.8125 -7.5t + t2 = -2.8125 The t term is -7.5t. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5t + 14.0625 + t2 = -2.8125 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = -2.8125 + 14.0625 Combine like terms: -2.8125 + 14.0625 = 11.25 14.0625 + -7.5t + t2 = 11.25 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (t + -3.75) equal to 3.354101966 and -3.354101966.Subproblem 1
t + -3.75 = 3.354101966 Simplifying t + -3.75 = 3.354101966 Reorder the terms: -3.75 + t = 3.354101966 Solving -3.75 + t = 3.354101966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = 3.354101966 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = 3.354101966 + 3.75 t = 3.354101966 + 3.75 Combine like terms: 3.354101966 + 3.75 = 7.104101966 t = 7.104101966 Simplifying t = 7.104101966Subproblem 2
t + -3.75 = -3.354101966 Simplifying t + -3.75 = -3.354101966 Reorder the terms: -3.75 + t = -3.354101966 Solving -3.75 + t = -3.354101966 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = -3.354101966 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = -3.354101966 + 3.75 t = -3.354101966 + 3.75 Combine like terms: -3.354101966 + 3.75 = 0.395898034 t = 0.395898034 Simplifying t = 0.395898034Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.104101966, 0.395898034}
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