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Simplifying 0 = -16t2 + 107t + 36 Reorder the terms: 0 = 36 + 107t + -16t2 Solving 0 = 36 + 107t + -16t2 Solving for variable 't'. Combine like terms: 0 + -36 = -36 -36 + -107t + 16t2 = 36 + 107t + -16t2 + -36 + -107t + 16t2 Reorder the terms: -36 + -107t + 16t2 = 36 + -36 + 107t + -107t + -16t2 + 16t2 Combine like terms: 36 + -36 = 0 -36 + -107t + 16t2 = 0 + 107t + -107t + -16t2 + 16t2 -36 + -107t + 16t2 = 107t + -107t + -16t2 + 16t2 Combine like terms: 107t + -107t = 0 -36 + -107t + 16t2 = 0 + -16t2 + 16t2 -36 + -107t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -36 + -107t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.25 + -6.6875t + t2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -6.6875t + 2.25 + t2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -6.6875t + t2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -6.6875t + t2 = 0 + 2.25 -6.6875t + t2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -6.6875t + t2 = 2.25 The t term is -6.6875t. Take half its coefficient (-3.34375). Square it (11.18066406) and add it to both sides. Add '11.18066406' to each side of the equation. -6.6875t + 11.18066406 + t2 = 2.25 + 11.18066406 Reorder the terms: 11.18066406 + -6.6875t + t2 = 2.25 + 11.18066406 Combine like terms: 2.25 + 11.18066406 = 13.43066406 11.18066406 + -6.6875t + t2 = 13.43066406 Factor a perfect square on the left side: (t + -3.34375)(t + -3.34375) = 13.43066406 Calculate the square root of the right side: 3.664787042 Break this problem into two subproblems by setting (t + -3.34375) equal to 3.664787042 and -3.664787042.Subproblem 1
t + -3.34375 = 3.664787042 Simplifying t + -3.34375 = 3.664787042 Reorder the terms: -3.34375 + t = 3.664787042 Solving -3.34375 + t = 3.664787042 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.34375' to each side of the equation. -3.34375 + 3.34375 + t = 3.664787042 + 3.34375 Combine like terms: -3.34375 + 3.34375 = 0.00000 0.00000 + t = 3.664787042 + 3.34375 t = 3.664787042 + 3.34375 Combine like terms: 3.664787042 + 3.34375 = 7.008537042 t = 7.008537042 Simplifying t = 7.008537042Subproblem 2
t + -3.34375 = -3.664787042 Simplifying t + -3.34375 = -3.664787042 Reorder the terms: -3.34375 + t = -3.664787042 Solving -3.34375 + t = -3.664787042 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.34375' to each side of the equation. -3.34375 + 3.34375 + t = -3.664787042 + 3.34375 Combine like terms: -3.34375 + 3.34375 = 0.00000 0.00000 + t = -3.664787042 + 3.34375 t = -3.664787042 + 3.34375 Combine like terms: -3.664787042 + 3.34375 = -0.321037042 t = -0.321037042 Simplifying t = -0.321037042Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.008537042, -0.321037042}
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