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Simplifying 0 = 3 + 75t + -16t2 Solving 0 = 3 + 75t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -75t + 16t2 = 3 + 75t + -16t2 + -3 + -75t + 16t2 Reorder the terms: -3 + -75t + 16t2 = 3 + -3 + 75t + -75t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -75t + 16t2 = 0 + 75t + -75t + -16t2 + 16t2 -3 + -75t + 16t2 = 75t + -75t + -16t2 + 16t2 Combine like terms: 75t + -75t = 0 -3 + -75t + 16t2 = 0 + -16t2 + 16t2 -3 + -75t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -75t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -4.6875t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -4.6875t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -4.6875t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -4.6875t + t2 = 0 + 0.1875 -4.6875t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -4.6875t + t2 = 0.1875 The t term is -4.6875t. Take half its coefficient (-2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. -4.6875t + 5.493164063 + t2 = 0.1875 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875t + t2 = 0.1875 + 5.493164063 Combine like terms: 0.1875 + 5.493164063 = 5.680664063 5.493164063 + -4.6875t + t2 = 5.680664063 Factor a perfect square on the left side: (t + -2.34375)(t + -2.34375) = 5.680664063 Calculate the square root of the right side: 2.383414371 Break this problem into two subproblems by setting (t + -2.34375) equal to 2.383414371 and -2.383414371.Subproblem 1
t + -2.34375 = 2.383414371 Simplifying t + -2.34375 = 2.383414371 Reorder the terms: -2.34375 + t = 2.383414371 Solving -2.34375 + t = 2.383414371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = 2.383414371 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = 2.383414371 + 2.34375 t = 2.383414371 + 2.34375 Combine like terms: 2.383414371 + 2.34375 = 4.727164371 t = 4.727164371 Simplifying t = 4.727164371Subproblem 2
t + -2.34375 = -2.383414371 Simplifying t + -2.34375 = -2.383414371 Reorder the terms: -2.34375 + t = -2.383414371 Solving -2.34375 + t = -2.383414371 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = -2.383414371 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = -2.383414371 + 2.34375 t = -2.383414371 + 2.34375 Combine like terms: -2.383414371 + 2.34375 = -0.039664371 t = -0.039664371 Simplifying t = -0.039664371Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.727164371, -0.039664371}
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