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Simplifying 16t2 + -8t + -24.7 = 0 Reorder the terms: -24.7 + -8t + 16t2 = 0 Solving -24.7 + -8t + 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'. -1.54375 + -0.5t + t2 = 0 Move the constant term to the right: Add '1.54375' to each side of the equation. -1.54375 + -0.5t + 1.54375 + t2 = 0 + 1.54375 Reorder the terms: -1.54375 + 1.54375 + -0.5t + t2 = 0 + 1.54375 Combine like terms: -1.54375 + 1.54375 = 0.00000 0.00000 + -0.5t + t2 = 0 + 1.54375 -0.5t + t2 = 0 + 1.54375 Combine like terms: 0 + 1.54375 = 1.54375 -0.5t + t2 = 1.54375 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 1.54375 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 1.54375 + 0.0625 Combine like terms: 1.54375 + 0.0625 = 1.60625 0.0625 + -0.5t + t2 = 1.60625 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 1.60625 Calculate the square root of the right side: 1.267379186 Break this problem into two subproblems by setting (t + -0.25) equal to 1.267379186 and -1.267379186.Subproblem 1
t + -0.25 = 1.267379186 Simplifying t + -0.25 = 1.267379186 Reorder the terms: -0.25 + t = 1.267379186 Solving -0.25 + t = 1.267379186 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 1.267379186 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 1.267379186 + 0.25 t = 1.267379186 + 0.25 Combine like terms: 1.267379186 + 0.25 = 1.517379186 t = 1.517379186 Simplifying t = 1.517379186Subproblem 2
t + -0.25 = -1.267379186 Simplifying t + -0.25 = -1.267379186 Reorder the terms: -0.25 + t = -1.267379186 Solving -0.25 + t = -1.267379186 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -1.267379186 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -1.267379186 + 0.25 t = -1.267379186 + 0.25 Combine like terms: -1.267379186 + 0.25 = -1.017379186 t = -1.017379186 Simplifying t = -1.017379186Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.517379186, -1.017379186}
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