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Simplifying 16t2 + -11t + -205 = 0 Reorder the terms: -205 + -11t + 16t2 = 0 Solving -205 + -11t + 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'. -12.8125 + -0.6875t + t2 = 0 Move the constant term to the right: Add '12.8125' to each side of the equation. -12.8125 + -0.6875t + 12.8125 + t2 = 0 + 12.8125 Reorder the terms: -12.8125 + 12.8125 + -0.6875t + t2 = 0 + 12.8125 Combine like terms: -12.8125 + 12.8125 = 0.0000 0.0000 + -0.6875t + t2 = 0 + 12.8125 -0.6875t + t2 = 0 + 12.8125 Combine like terms: 0 + 12.8125 = 12.8125 -0.6875t + t2 = 12.8125 The t term is -0.6875t. Take half its coefficient (-0.34375). Square it (0.1181640625) and add it to both sides. Add '0.1181640625' to each side of the equation. -0.6875t + 0.1181640625 + t2 = 12.8125 + 0.1181640625 Reorder the terms: 0.1181640625 + -0.6875t + t2 = 12.8125 + 0.1181640625 Combine like terms: 12.8125 + 0.1181640625 = 12.9306640625 0.1181640625 + -0.6875t + t2 = 12.9306640625 Factor a perfect square on the left side: (t + -0.34375)(t + -0.34375) = 12.9306640625 Calculate the square root of the right side: 3.595923256 Break this problem into two subproblems by setting (t + -0.34375) equal to 3.595923256 and -3.595923256.Subproblem 1
t + -0.34375 = 3.595923256 Simplifying t + -0.34375 = 3.595923256 Reorder the terms: -0.34375 + t = 3.595923256 Solving -0.34375 + t = 3.595923256 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.34375' to each side of the equation. -0.34375 + 0.34375 + t = 3.595923256 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + t = 3.595923256 + 0.34375 t = 3.595923256 + 0.34375 Combine like terms: 3.595923256 + 0.34375 = 3.939673256 t = 3.939673256 Simplifying t = 3.939673256Subproblem 2
t + -0.34375 = -3.595923256 Simplifying t + -0.34375 = -3.595923256 Reorder the terms: -0.34375 + t = -3.595923256 Solving -0.34375 + t = -3.595923256 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.34375' to each side of the equation. -0.34375 + 0.34375 + t = -3.595923256 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + t = -3.595923256 + 0.34375 t = -3.595923256 + 0.34375 Combine like terms: -3.595923256 + 0.34375 = -3.252173256 t = -3.252173256 Simplifying t = -3.252173256Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.939673256, -3.252173256}
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