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Simplifying 0 = -16t2 + 14t + 975 Reorder the terms: 0 = 975 + 14t + -16t2 Solving 0 = 975 + 14t + -16t2 Solving for variable 't'. Combine like terms: 0 + -975 = -975 -975 + -14t + 16t2 = 975 + 14t + -16t2 + -975 + -14t + 16t2 Reorder the terms: -975 + -14t + 16t2 = 975 + -975 + 14t + -14t + -16t2 + 16t2 Combine like terms: 975 + -975 = 0 -975 + -14t + 16t2 = 0 + 14t + -14t + -16t2 + 16t2 -975 + -14t + 16t2 = 14t + -14t + -16t2 + 16t2 Combine like terms: 14t + -14t = 0 -975 + -14t + 16t2 = 0 + -16t2 + 16t2 -975 + -14t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -975 + -14t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -60.9375 + -0.875t + t2 = 0 Move the constant term to the right: Add '60.9375' to each side of the equation. -60.9375 + -0.875t + 60.9375 + t2 = 0 + 60.9375 Reorder the terms: -60.9375 + 60.9375 + -0.875t + t2 = 0 + 60.9375 Combine like terms: -60.9375 + 60.9375 = 0.0000 0.0000 + -0.875t + t2 = 0 + 60.9375 -0.875t + t2 = 0 + 60.9375 Combine like terms: 0 + 60.9375 = 60.9375 -0.875t + t2 = 60.9375 The t term is -0.875t. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875t + 0.19140625 + t2 = 60.9375 + 0.19140625 Reorder the terms: 0.19140625 + -0.875t + t2 = 60.9375 + 0.19140625 Combine like terms: 60.9375 + 0.19140625 = 61.12890625 0.19140625 + -0.875t + t2 = 61.12890625 Factor a perfect square on the left side: (t + -0.4375)(t + -0.4375) = 61.12890625 Calculate the square root of the right side: 7.818497698 Break this problem into two subproblems by setting (t + -0.4375) equal to 7.818497698 and -7.818497698.Subproblem 1
t + -0.4375 = 7.818497698 Simplifying t + -0.4375 = 7.818497698 Reorder the terms: -0.4375 + t = 7.818497698 Solving -0.4375 + t = 7.818497698 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + t = 7.818497698 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + t = 7.818497698 + 0.4375 t = 7.818497698 + 0.4375 Combine like terms: 7.818497698 + 0.4375 = 8.255997698 t = 8.255997698 Simplifying t = 8.255997698Subproblem 2
t + -0.4375 = -7.818497698 Simplifying t + -0.4375 = -7.818497698 Reorder the terms: -0.4375 + t = -7.818497698 Solving -0.4375 + t = -7.818497698 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + t = -7.818497698 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + t = -7.818497698 + 0.4375 t = -7.818497698 + 0.4375 Combine like terms: -7.818497698 + 0.4375 = -7.380997698 t = -7.380997698 Simplifying t = -7.380997698Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.255997698, -7.380997698}
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