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Simplifying 16t2 + -27t + -3 = 0 Reorder the terms: -3 + -27t + 16t2 = 0 Solving -3 + -27t + 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'. -0.1875 + -1.6875t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -1.6875t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -1.6875t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -1.6875t + t2 = 0 + 0.1875 -1.6875t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -1.6875t + t2 = 0.1875 The t term is -1.6875t. Take half its coefficient (-0.84375). Square it (0.7119140625) and add it to both sides. Add '0.7119140625' to each side of the equation. -1.6875t + 0.7119140625 + t2 = 0.1875 + 0.7119140625 Reorder the terms: 0.7119140625 + -1.6875t + t2 = 0.1875 + 0.7119140625 Combine like terms: 0.1875 + 0.7119140625 = 0.8994140625 0.7119140625 + -1.6875t + t2 = 0.8994140625 Factor a perfect square on the left side: (t + -0.84375)(t + -0.84375) = 0.8994140625 Calculate the square root of the right side: 0.948374432 Break this problem into two subproblems by setting (t + -0.84375) equal to 0.948374432 and -0.948374432.Subproblem 1
t + -0.84375 = 0.948374432 Simplifying t + -0.84375 = 0.948374432 Reorder the terms: -0.84375 + t = 0.948374432 Solving -0.84375 + t = 0.948374432 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.84375' to each side of the equation. -0.84375 + 0.84375 + t = 0.948374432 + 0.84375 Combine like terms: -0.84375 + 0.84375 = 0.00000 0.00000 + t = 0.948374432 + 0.84375 t = 0.948374432 + 0.84375 Combine like terms: 0.948374432 + 0.84375 = 1.792124432 t = 1.792124432 Simplifying t = 1.792124432Subproblem 2
t + -0.84375 = -0.948374432 Simplifying t + -0.84375 = -0.948374432 Reorder the terms: -0.84375 + t = -0.948374432 Solving -0.84375 + t = -0.948374432 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.84375' to each side of the equation. -0.84375 + 0.84375 + t = -0.948374432 + 0.84375 Combine like terms: -0.84375 + 0.84375 = 0.00000 0.00000 + t = -0.948374432 + 0.84375 t = -0.948374432 + 0.84375 Combine like terms: -0.948374432 + 0.84375 = -0.104624432 t = -0.104624432 Simplifying t = -0.104624432Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.792124432, -0.104624432}
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