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Simplifying 16t2 + -235t + 151 = 0 Reorder the terms: 151 + -235t + 16t2 = 0 Solving 151 + -235t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 9.4375 + -14.6875t + t2 = 0 Move the constant term to the right: Add '-9.4375' to each side of the equation. 9.4375 + -14.6875t + -9.4375 + t2 = 0 + -9.4375 Reorder the terms: 9.4375 + -9.4375 + -14.6875t + t2 = 0 + -9.4375 Combine like terms: 9.4375 + -9.4375 = 0.0000 0.0000 + -14.6875t + t2 = 0 + -9.4375 -14.6875t + t2 = 0 + -9.4375 Combine like terms: 0 + -9.4375 = -9.4375 -14.6875t + t2 = -9.4375 The t term is -14.6875t. Take half its coefficient (-7.34375). Square it (53.93066406) and add it to both sides. Add '53.93066406' to each side of the equation. -14.6875t + 53.93066406 + t2 = -9.4375 + 53.93066406 Reorder the terms: 53.93066406 + -14.6875t + t2 = -9.4375 + 53.93066406 Combine like terms: -9.4375 + 53.93066406 = 44.49316406 53.93066406 + -14.6875t + t2 = 44.49316406 Factor a perfect square on the left side: (t + -7.34375)(t + -7.34375) = 44.49316406 Calculate the square root of the right side: 6.670319637 Break this problem into two subproblems by setting (t + -7.34375) equal to 6.670319637 and -6.670319637.Subproblem 1
t + -7.34375 = 6.670319637 Simplifying t + -7.34375 = 6.670319637 Reorder the terms: -7.34375 + t = 6.670319637 Solving -7.34375 + t = 6.670319637 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.34375' to each side of the equation. -7.34375 + 7.34375 + t = 6.670319637 + 7.34375 Combine like terms: -7.34375 + 7.34375 = 0.00000 0.00000 + t = 6.670319637 + 7.34375 t = 6.670319637 + 7.34375 Combine like terms: 6.670319637 + 7.34375 = 14.014069637 t = 14.014069637 Simplifying t = 14.014069637Subproblem 2
t + -7.34375 = -6.670319637 Simplifying t + -7.34375 = -6.670319637 Reorder the terms: -7.34375 + t = -6.670319637 Solving -7.34375 + t = -6.670319637 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.34375' to each side of the equation. -7.34375 + 7.34375 + t = -6.670319637 + 7.34375 Combine like terms: -7.34375 + 7.34375 = 0.00000 0.00000 + t = -6.670319637 + 7.34375 t = -6.670319637 + 7.34375 Combine like terms: -6.670319637 + 7.34375 = 0.673430363 t = 0.673430363 Simplifying t = 0.673430363Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.014069637, 0.673430363}
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