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Simplifying 253t + -16t2 = 151 Solving 253t + -16t2 = 151 Solving for variable 't'. Reorder the terms: -151 + 253t + -16t2 = 151 + -151 Combine like terms: 151 + -151 = 0 -151 + 253t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 9.4375 + -15.8125t + t2 = 0 Move the constant term to the right: Add '-9.4375' to each side of the equation. 9.4375 + -15.8125t + -9.4375 + t2 = 0 + -9.4375 Reorder the terms: 9.4375 + -9.4375 + -15.8125t + t2 = 0 + -9.4375 Combine like terms: 9.4375 + -9.4375 = 0.0000 0.0000 + -15.8125t + t2 = 0 + -9.4375 -15.8125t + t2 = 0 + -9.4375 Combine like terms: 0 + -9.4375 = -9.4375 -15.8125t + t2 = -9.4375 The t term is -15.8125t. Take half its coefficient (-7.90625). Square it (62.50878906) and add it to both sides. Add '62.50878906' to each side of the equation. -15.8125t + 62.50878906 + t2 = -9.4375 + 62.50878906 Reorder the terms: 62.50878906 + -15.8125t + t2 = -9.4375 + 62.50878906 Combine like terms: -9.4375 + 62.50878906 = 53.07128906 62.50878906 + -15.8125t + t2 = 53.07128906 Factor a perfect square on the left side: (t + -7.90625)(t + -7.90625) = 53.07128906 Calculate the square root of the right side: 7.285004397 Break this problem into two subproblems by setting (t + -7.90625) equal to 7.285004397 and -7.285004397.Subproblem 1
t + -7.90625 = 7.285004397 Simplifying t + -7.90625 = 7.285004397 Reorder the terms: -7.90625 + t = 7.285004397 Solving -7.90625 + t = 7.285004397 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.90625' to each side of the equation. -7.90625 + 7.90625 + t = 7.285004397 + 7.90625 Combine like terms: -7.90625 + 7.90625 = 0.00000 0.00000 + t = 7.285004397 + 7.90625 t = 7.285004397 + 7.90625 Combine like terms: 7.285004397 + 7.90625 = 15.191254397 t = 15.191254397 Simplifying t = 15.191254397Subproblem 2
t + -7.90625 = -7.285004397 Simplifying t + -7.90625 = -7.285004397 Reorder the terms: -7.90625 + t = -7.285004397 Solving -7.90625 + t = -7.285004397 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.90625' to each side of the equation. -7.90625 + 7.90625 + t = -7.285004397 + 7.90625 Combine like terms: -7.90625 + 7.90625 = 0.00000 0.00000 + t = -7.285004397 + 7.90625 t = -7.285004397 + 7.90625 Combine like terms: -7.285004397 + 7.90625 = 0.621245603 t = 0.621245603 Simplifying t = 0.621245603Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.191254397, 0.621245603}
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